Math 2650 - Linear Differential EquationsA. J. MeirCopyright (C) A. J. Meir. All rights reserved.This worksheet is for educational use only. No part of this publication may be reproduced or transmitted for profit in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system without prior written permission from the author. Not for profit distribution of the software is allowed without prior written permission, providing that the worksheet is not modified in any way and full credit to the author is acknowledged.

We consider equations of the typeNiMlIm1HNiMvLCYqKCUiZEciIiMlInhHIiIiKiQlI2R0R0YnISIiRiklI2t4R0YpKiYlIkZHRiktJSRjb3NHNiMqJiUmb21lZ2FHRiklInRHRilGKQ==.For example take NiMvJSJtRyIiIg==, NiMvJSJrRyIiKg==, and NiMvJSJGRyIiJQ== (the roots of the characteristic polynomial are NiMqJiIiJCIiIiUiSUdGJQ== and NiMsJComIiIkIiIiJSJJR0YmISIi)NiMvLCYqKCUiZEciIiMlInhHIiIiKiQlI2R0R0YnISIiRikqJiIiKkYpRihGKUYpKiYiIiVGKS0lJGNvc0c2IyomJSZvbWVnYUdGKSUidEdGKUYpwith initial conditionsNiMvLSUieEc2IyIiIUYn and NiMqJiUjZHhHIiIiJSNkdEchIiI= (0)=0.restart:with(DEtools):dsolve({D(D(x))(t)+9*x(t)=4*cos(omega*t),x(0)=0,D(x)(0)=0},x(t));

NiMvLUkieEc2IjYjSSJ0R0YmLCYqJi1JJGNvc0c2JEkqcHJvdGVjdGVkR0YuSShfc3lzbGliR0YmNiMsJEYoIiIkIiIiLCYhIipGMyokSSZvbWVnYUdGJiIiI0YzISIiIiIlKiYtRiw2IyomRjdGM0YoRjNGM0Y0RjkhIiU=

That is given a periodic function of the formNiMvLSUiZkc2IyUidEcsJiomJSJhRyIiIi0lJGNvc0c2IyomJSZvbWVnYUdGK0YnRitGK0YrKiYlImJHRistJSRzaW5HRi5GK0Yrwe can write it asNiMvLSUiZkc2IyUidEcqJiUiQUciIiItJSRjb3NHNiMsJiomJSZvbWVnYUdGKkYnRipGKiUmZGVsdGFHISIiRio=whereNiMvJSJBRy0lJXNxcnRHNiMsJiokJSJhRyIiIyIiIiokJSJiR0YrRiw=andNiMvJSZkZWx0YUctJSdhcmN0YW5HNiMqJiUiYkciIiIlImFHISIi(note this last equation has two solutions which differ by NiMlI1BpRw==, you must chose the correct solution).Also recall the two trigonometric identitiesNiMvLCYtJSRjb3NHNiMlJmFscGhhRyIiIi1GJjYjJSViZXRhRyEiIiwkKigiIiNGKS0lJHNpbkc2IyomLCZGKEYpRixGKUYpRjBGLUYpLUYyNiMqJiwmRihGKUYsRi1GKUYwRi1GKUYtandNiMvLCYtJSRzaW5HNiMlJmFscGhhRyIiIi1GJjYjJSViZXRhRyEiIiooIiIjRiktJSRjb3NHNiMqJiwmRihGKUYsRilGKUYvRi1GKS1GJjYjKiYsJkYoRilGLEYtRilGL0YtRik=using these identities we can often rewrite periodic functions to better see the phenomenon of beats.

sol(t):=-8/(-9+omega^2)*sin((3-omega)*t/2)*sin((3+omega)*t/2);

NiM+LUkkc29sRzYiNiNJInRHRiYsJCooLCYhIioiIiIqJEkmb21lZ2FHRiYiIiNGLSEiIi1JJHNpbkc2JEkqcHJvdGVjdGVkR0Y1SShfc3lzbGliR0YmNiMsJComLCYiIiRGLUYvRjFGLUYoRi0jRi1GMEYtLUYzNiMsJComLCZGO0YtRi9GLUYtRihGLUY8Ri0hIik=

env(t):=-8/(-9+omega^2)*sin((3-omega)*t/2);

NiM+LUkkZW52RzYiNiNJInRHRiYsJComLCYhIioiIiIqJEkmb21lZ2FHRiYiIiNGLSEiIi1JJHNpbkc2JEkqcHJvdGVjdGVkR0Y1SShfc3lzbGliR0YmNiMsJComLCYiIiRGLUYvRjFGLUYoRi0jRi1GMEYtISIp

omega:=1:plot([sol(t),env(t),-env(t)],t=0..20,color=[black,red,red]);

-%%PLOTG6'-%'CURVESG6$7[^l7$$""!F+F*7$$"3GLLL3x&)*3"!#=$"3<')=lH,:_B!#>7$$"3dmmm;arz@F/$"3F?#oi>u98*F27$$"3')*****\7t&pKF/$"3lIv#elGO&>F/7$$"39LLLL3VfVF/$"3'*["[HAFEB$F/7$$"3Kmm"z>5xI&F/$"3=uh=^0m>WF/7$$"3\****\i&*)fD'F/$"3nRg8v&*HfbF/7$$"3mKL3F*oU?(F/$"3dmx)\*zVTlF/7$$"3%pmm;H[D:)F/$"3CqA?#4IgE(F/7$$"3$4+DJ&zw&o)F/$"33BZ;->rGvF/7$$"3#QL$e9w)*=#*F/$"3"*HXZ-nVswF/7$$"3D+DJXuf&[*F/$"3kk]^P4&pp(F/7$$"3qm;/ws?_(*F/$"3w9K'\+9))o(F/7$$"3V$3x1r")=+"!#<$"3-F#pC_cuk(F/7$$"3'****\PpU&G5Fgo$"3()pjA&=5Dd(F/7$$"3am;/Em=N6Fgo$"3Dchy4'Gm$pF/7$$"3MLLLe0$=C"Fgo$"3$\hCI%)>py&F/7$$"3ELL3xf]&H"Fgo$"3mC(oniC[.&F/7$$"3SLL$eR"=\8Fgo$"3,6I@v;r$=%F/7$$"3cLLe9o&GS"Fgo$"3#p%=a6;i\KF/7$$"3[LLLLA`c9Fgo$"3?(*ySy"p1D#F/7$$"3TLL3_w?5:Fgo$"3:Sae#)>f17F/7$$"3bLL$32$)Qc"Fgo$"3CBt=*4uDQ"F27$$"3qLLe*[evh"Fgo$!3'4U<H#efG$*F27$$"3iLLL3RBr;Fgo$!3aJO8NV@&)>F/7$$"37+v=<UlC<Fgo$!3?2:F]h/$*HF/7$$"3#omTg_u!y<Fgo$!3+7\#eBA;%RF/7$$"3`Le*[$[\J=Fgo$!3UZ"RYl:E"[F/7$$"3B++vV^"\)=Fgo$!3gic[W4i*e&F/7$$"3WL$e9wb<*>Fgo$!3**41)[s9!3oF/7$$"3imm;zjf)4#Fgo$!3h;%)34Gx<vF/7$$"39L$e96gL7#Fgo$!3>/Eh+5\0wF/7$$"34++vVQ7[@Fgo$!3f#[$ef27kwF/7$$"3/n;/wv)G<#Fgo$!3s:+iJ9&Qp(F/7$$"3aLLL38l(>#Fgo$!3_&p^GeB]p(F/7$$"3dmm"HxyrC#Fgo$!3hS(eQu'z8wF/7$$"3-++]Piq'H#Fgo$!3`P]^Xd3EuF/7$$"3[mmmm6w&R#Fgo$!3bWF"3G#fknF/7$$"3ULL$e4;[\#Fgo$!3O*y*Q2Q0'z&F/7$$"37++]P<Q(f#Fgo$!3TJ*fcglme%F/7$$"3#omm"zt%**p#Fgo$!3B=@/^IH.LF/7$$"3`LL$3-8D!GFgo$!3V[V*GVAn3#F/7$$"3!)****\i'y]!HFgo$!3Y!)fxa<]n5F/7$$"3gLL$e>_6,$Fgo$!3%*e\or3%\N$F27$$"3'pmm"HdA<JFgo$!3SkwJel!p="!#?7$$"3I++]7TuVJFgo$!3[y')Rv^^d#*!#B7$$"3jLL$e\i-<$Fgo$!3*=3\#fRzU;Fey7$$"3'pmm"z3y'>$Fgo$!3h5()>sQ.wgFey7$$"3K++]i#*HBKFgo$!3))zHA=4yF8F27$$"3*pmm"HgLwKFgo$!38M,RB%=ld$F27$$"3oLL$ezs$HLFgo$!3oiF!)>GDZoF27$$"3=+++]h5NMFgo$!3/Fm"*yR\-;F/7$$"3qmm;/&R3a$Fgo$!3?LV\0lX%y#F/7$$"3ALLLeGdYOFgo$!3'H+G'*)oy'4%F/7$$"3=++]7iI_PFgo$!3rx`9+E4)Q&F/7$$"3'omTN'f1hQFgo$!3+w9gD')oKlF/7$$"3+MLe9d#)pRFgo$!3&*oMCQ$e.M(F/7$$"3omT5!f0U-%Fgo$!3$[&G8[`ZyvF/7$$"3B+]ilaeySFgo$!3EX#Q*G[G!p(F/7$$"3-<aQ.ax0TFgo$!3;Wh)f^%='p(F/7$$"3!Q$e9T`'H8%Fgo$!3r">@))4`xm(F/7$$"3e]i!*y_:gTFgo$!3]/t;4L^/wF/7$$"3Onmm;_M(=%Fgo$!3q>v@!R2i](F/7$$"3?MLek39$G%Fgo$!3WFg?)*Q(>)oF/7$$"3/,+]7l$*yVFgo$!3$eurGac[%eF/7$$"3YM$ekLMoU%Fgo$!30ez1isv'=&F/7$$"3)ym;/;KZZ%Fgo$!3&zb#[ewaZWF/7$$"3I,]P%)*HE_%Fgo$!3i/f1HrAQOF/7$$"3$QLL$3y_qXFgo$!3&4:Kyv!>rFF/7$$"3%pmTNT\Wi%Fgo$!3Y:J@Tk(Hu"F/7$$"3$4+](=5PyYFgo$!3!Q@3<[6Wz'F27$$"31M$eRi#HKZFgo$"3x"3Jc@*))yRF27$$"3;nm;HU@'y%Fgo$"3(zb,a%)QrY"F/7$$"3G+]PMe8S[Fgo$"3c]'*3ozj1DF/7$$"3QLLeRu0%*[Fgo$"3s*Q6ydna\$F/7$$"3Rn;zW!zz%\Fgo$"3%=SF2-*)RT%F/7$$"3]+++]1!>+&Fgo$"3mU[,<&QVC&F/7$$"3Y+++vm=5^Fgo$"3Z0C')y"o]e'F/7$$"3S++++FZ=_Fgo$"3K"[4-5xoT(F/7$$"3%3+]i?WbC&Fgo$"3av&**)o6@RvF/7$$"3Q++]7dhs_Fgo$"3HIZL?ctEwF/7$$"3#****\(=so*H&Fgo$"3%QL+!p4bzwF/7$$"3O+++D(enK&Fgo$"3K!G)[H^(zp(F/7$$"3z++DJ-$QN&Fgo$"3D-"HE$3a#o(F/7$$"3L++]P<!4Q&Fgo$"3)o;OUj"*Rj(F/7$$"3))***\PCtzS&Fgo$"3k(GCJawKb(F/7$$"3J+++]Z/NaFgo$"3Gn/;/LaTuF/7$$"3h*******R)RRbFgo$"3q`g+H@OZnF/7$$"3!)******\?vVcFgo$"3YieT`"G\r&F/7$$"3)********p0"[dFgo$"3Xk*)eC'=LZ%F/7$$"3;+++]$fC&eFgo$"3GOVMyh<oJF/7$$"3xL$e9YAs%fFgo$"3@Na]Z'GA0#F/7$$"3Qnm"Hd&)>/'Fgo$"3%Q+F:XA"36F/7$$"35+]P%o[n8'Fgo$"3!R@0Z3&f7UF27$$"3qLL$ez6:B'Fgo$"34;>?>.VG`Fey7$$"3.<a8ACofiFgo$"3E:1CYFE/6Fey7$$"3P+vV[I&yG'Fgo$"37&o*esD[dV!#A7$$"3q$eRZnBgJ'Fgo$"3xn<=2$zZ:#Fey7$$"3/n;/,V>WjFgo$"3OX<t.28@uFey7$$"3rLek`b`+kFgo$"3+<M3)pSFs#F27$$"3P++D1o(oX'Fgo$"3c8<*)*pOM)eF27$$"3rL$e9Jf&plFgo$"3eL))f8#f3`"F/7$$"3/nmm;=C#o'Fgo$"3v*Qo[$z;#y#F/7$$"3!pmm"z')pxnFgo$"3+w6y'>r_'RF/7$$"3knmmTb:toFgo$"3pIXN6EzV^F/7$$"3]nm;/ChopFgo$"3;"pV*>0$R?'F/7$$"3Mnmmm#pS1(Fgo$"3#>_a![()yQqF/7$$"3GMeky()e>rFgo$"30nE#H$=z$Q(F/7$$"3K+]i!H3^<(Fgo$"3mO[w8B%og(F/7$$"3"He9m/oG?(Fgo$"3ml9RK>&*owF/7$$"3QmTg-yiIsFgo$"3yNd/RWd'p(F/7$$"3%)\PfevQesFgo$"3uv[o#4J))o(F/7$$"3JLLe9t9'G(Fgo$"3u28uJW2XwF/7$$"3=n;aQj=(R(Fgo$"3N%G4+,'H0rF/7$$"3<++]i`A3vFgo$"3o#HH**fL'**fF/7$$"3xK3-Q&ptb(Fgo$"3zCiB;JDY`F/7$$"3Gm;a8P^1wFgo$"30)oEsMa]g%F/7$$"3x*\i!*)ylbwFgo$"3\q()4;db(y$F/7$$"3GLLek?![q(Fgo$"3L&)4%)*4uo!HF/7$$"3xmT5Si%Rv(Fgo$"3uvl(*)Q^u(>F/7$$"3G+]i:/4.yFgo$"3vorB4Cv95F/7$$"3xLe9"fMA&yFgo$"3=^TR:K2%\$Fey7$$"3Rmmmm(y8!zFgo$!34h,.*=1YX*F27$$"3.Me9;xHbzFgo$!3_%G$\sJ;-?F/7$$"3y+]ilm@4!)Fgo$!3Ea.-ShK=IF/7$$"3anT5:c8j!)Fgo$!3fiC")y@itRF/7$$"3IMLekX0<")Fgo$!3a1P&Q%4E\[F/7$$"3!ymTNY#*[A)Fgo$!3mQ6=IU(oH'F/7$$"3K,+]i.tK$)Fgo$!3HA^G-O:esF/7$$"39+]7`R2%Q)Fgo$!34!Q2fD;r_(F/7$$"3u++vVvTN%)Fgo$!3H9G00a/rwF/7$$"3:+D1R$*3h%)Fgo$!3%)3#zg!=Q'p(F/7$$"3N,]PM6w'[)Fgo$!3AS")*Gf@6p(F/7$$"3w+voHHV7&)Fgo$!3lA#)yZk%el(F/7$$"3<+++DZ5Q&)Fgo$!3ES4[EdI"f(F/7$$"3Q,+D1>zS')Fgo$!3P'*eB([Z51(F/7$$"3!3++v3zMu)Fgo$!3l)*R))Ry,ihF/7$$"3rn;a)QA1&))Fgo$!3=&3DS%Rq`\F/7$$"3jMLe*olx&*)Fgo$!3]>:+@/')>OF/7$$"3b,]i!**3\1*Fgo$!3K,fh*yR8K#F/7$$"3Yomm"H_?<*Fgo$!3t#f7%)))=2@"F/7$$"3@n;a)GV/F*Fgo$!3[7H<C)f*pYF27$$"3tnmT&GM)o$*Fgo$!3QS\TJ,3ViFey7$$"3+oT&QyH!=%*Fgo$!3S[o(RsKs5*F[jl7$$"3Fo;H#GDsY*Fgo$!3'**>H#4D9)f$Fey7$$"3vm"H2y?k^*Fgo$!3s1caec&zm"F27$$"3,nm;zihl&*Fgo$!3LX?i6c!>!RF27$$"3lK$e9EW<n*Fgo$!3k;caZ=)*e6F/7$$"33++vVA(yx*Fgo$!3J#pg%R"[SC#F/7$$"3\n;/E-+%))*Fgo$!39i/y7;LANF/7$$"39LLL3#G,***Fgo$!3GSNs.4kY[F/7$$"3@L3_Nl.55!#;$!3i_f5wsM.hF/7$$"3HL$3-Dg5-"F][n$!3)[;sSazS2(F/7$$"3K$3_v5sl-"F][n$!3H4(y-?$y1uF/7$$"3OLe*['R3K5F][n$!3qI9B%4\#=wF/7$$"3Q3xc$*)R[."F][n$!3sGm6qF*\n(F/7$$"3S$eRA#efP5F][n$!3uf')\`)3wp(F/7$$"3Ue9"4v^./"F][n$!3[j&*))H%o_o(F/7$$"3WLLezw5V5F][n$!3%=lqy+otj(F/7$$"3<+]ibQq_5F][n$!3WPi*\)y$)*=(F/7$$"3tmmmJ+Ii5F][n$!3Gs+9)*zf:jF/7$$"35+vo>")4n5F][n$!3)f())=[ppHdF/7$$"3HL$3x?'*=2"F][n$!3Rwbw:mfa]F/7$$"3mm"HdH%pw5F][n$!3r(p.T#)[+I%F/7$$"3.++v$Q#\"3"F][n$!30N=>#*3RxMF/7$$"3p;/E]Wn'3"F][n$!3I#)=![#Q1FDF/7$$"3OL3x;l&=4"F][n$!3_DVUvObH:F/7$$"3-]7G$eQq4"F][n$!3g1)yc2jR.&F27$$"3nm;z\1A-6F][n$"39joYqe.A`F27$$"3L$3-jr-u5"F][n$"3Eik)="3#yb"F/7$$"3++D"Gy%e76F][n$"3By03)GjUb#F/7$$"3m;HK\ow<6F][n$"33=dru+-.NF/7$$"3]LL$e"*[H7"F][n$"3X"=o2-$p'Q%F/7$$"3"o;/w\-$G6F][n$"3I7%4hQ<W@&F/7$$"37+]PzglL6F][n$"3s9GI63NSfF/7$$"3WLe9h'4!R6F][n$"3tbn\N1j^lF/7$$"3wmm"HCjV9"F][n$"3EJw+9dBQqF/7$$"32+voCor\6F][n$"3cI+l')zA$R(F/7$$"3RL$ekSq]:"F][n$"3hwqR]]"Hh(F/7$$"30]PM(>Zx:"F][n$"3"e4#QISxrwF/7$$"3qm"H#))RUg6F][n$"3!HYExfHpp(F/7$$"3O$e9"z25j6F][n$"3GJ)*oZW&))o(F/7$$"3-+++qvxl6F][n$"3"*ecm?PA[wF/7$$"3;+]iSCDw6F][n$"3]_w6kTS&>(F/7$$"38++D6ts'="F][n$"3"oaAv,_'RjF/7$$"35+](==-s>"F][n$"3AJzuPm'e>&F/7$$"31++]_qn27F][n$"3*f6EeY3N!RF/7$$"3;+vVG?"y@"F][n$"3n2,qdw'Hl#F/7$$"33+]P/q%zA"F][n$"3%zYm$)>+h`"F/7$$"3,+DJ!)>3Q7F][n$"3/s*QF,7.p'F27$$"36++Dcp@[7F][n$"3#[HZ%QQg49F27$$"31DJ&pCI5D"F][n$"36KKSs'=3F'Fey7$$"3,]ilPN%QD"F][n$"3+x&y*z-uf:Fey7$$"3'\Pf$Golc7F][n$"33v$o^+DY"y!#D7$$"33+D1>,Zf7F][n$"3CNka&ppTg"Fey7$$"3;](o/q'4l7F][n$"3!eb1tK#zA9F27$$"31+](=GB2F"F][n$"3UP%GXD2K!RF27$$"3.+voWk(>G"F][n$"3+goIs6y;7F/7$$"3+++]2'HKH"F][n$"3c`oMx:3"R#F/7$$"3am;zu5M.8F][n$"3#R")*3H'4-i$F/7$$"3ELL3UDX88F][n$"3@pT"3NG3)[F/7$$"3)***\P4ScB8F][n$"39%e0=&oaPgF/7$$"3_mmmwanL8F][n$"3")>8Es-(4'pF/7$$"3=L$e9bt!R8F][n$"3!p8UpN%))=tF/7$$"3$)***\iirWM"F][n$"3CxZ/&[IUc(F/7$$"3CLekj1<Z8F][n$"3:%><K9%4TwF/7$$"3mm;/,(p)\8F][n$"3A)\!pQz'eo(F/7$$"32+vVQ(oDN"F][n$"3M8&RFrLwp(F/7$$"3JLL$exn_N"F][n$"3T7KIdpnvwF/7$$"3zmmTDR1m8F][n$"3hE/D#>7PC(F/7$$"35+++v+'oP"F][n$"3OQK<S+GqiF/7$$"3q;H2L:v"Q"F][n$"31;K;ow8kcF/7$$"3HLe9"*Hk'Q"F][n$"3e&HY_=ei'\F/7$$"33](=#\W`"R"F][n$"3kbW=dI<(=%F/7$$"3om;H2fU'R"F][n$"3_09Mn")4RLF/7$$"3F$ek`O<8S"F][n$"3'QD7H2#oNCF/7$$"3/+vVB)3iS"F][n$"3kC-#feB<\"F/7$$"3k;/^"G+6T"F][n$"3T\N%RBZ'G_F27$$"3CLLeR<*fT"F][n$!34,wS'*RMZXF27$$"3i;/E&RR8U"F][n$!3UkpmG:B9:F/7$$"3***\P40(oE9F][n$!3DJ6Fq(HNa#F/7$$"3O$e9mqM?V"F][n$!37t$)e/PEANF/7$$"3um;HiBQP9F][n$!3Y36=JVKJWF/7$$"36](oz,IFW"F][n$!3d&*G#QgKLD&F/7$$"3\Lektw2[9F][n$!3"[z6cqoI(fF/7$$"3'o"HKH`U`9F][n$!3CtzK)3Yyd'F/7$$"3B+++&)Hxe9F][n$!3w9'=zr?y0(F/7$$"3g$eRAr/QY"F][n$!3h@,K!R!Q*Q(F/7$$"3ym"z%Rk$)o9F][n$!3KKmg#R59g(F/7$$"3Ye*)4.BNr9F][n$!3(4;8K:nBm(F/7$$"3'*\(=n;oQZ"F][n$!3CmM/xb[$p(F/7$$"3kT&Q..%Qw9F][n$!3yW-S\y6&p(F/7$$"3KL$eR*)**)y9F][n$!3(QUvO)\xnwF/7$$"30+vV[L'*)["F][n$!3M^HAjbA%G(F/7$$"3gmm"H!o-*\"F][n$!3(4r&>:ZI;lF/7$$"3*)****\7ga4:F][n$!36o-jO$o)3aF/7$$"3PLL3A_1?:F][n$!3o86el90ETF/7$$"3%omm;V%eI:F][n$!3;lc'ylS!>GF/7$$"39++DTO5T:F][n$!3n#pu)pV<P;F/7$$"3vmTN"4)Q^:F][n$!3#H="QO&)z*H(F27$$"3OL$e9as;c"F][n$!3?^q/y"\Ll"F27$$"3-vV)RlVUc"F][n$!3o)H@l+<ob)Fey7$$"3n;/^mZ"oc"F][n$!3Uus\SzPmJFey7$$"3Kek.zeQp:F][n$!3@6wD/i1yR!#@7$$"3(**\i:*p&>d"F][n$!3]USH_H)Rp#F]ho7$$"3G$e9m@*4x:F][n$!3!=S&*3b7!>zFey7$$"3emmmT9C#e"F][n$!3a7Ki#*)G8f#F27$$"3y*\7yI3If"F][n$!3KI-E@@xn%*F27$$"3;L$eR<vPg"F][n$!3**=M![$HX%)>F/7$$"3`mT5S?a9;F][n$!3fabdC(o8D$F/7$$"3"****\i!*3`i"F][n$!39vPxA7*zf%F/7$$"39L3-y'ycj"F][n$!3thlwD_Z=eF/7$$"3rm;z\%[gk"F][n$!3"p"4H(RV+#oF/7$$"3H+Dc@#=kl"F][n$!3_ju'*em0yuF/7$$"3_LLL$*zym;F][n$!3E\)ptQ9vp(F/7$$"3aL$3Fe#Rx;F][n$!3\WPeC!*Q5uF/7$$"3bLL3sr*zo"F][n$!3WB!QeN%3&f'F/7$$"3cL3xm%*H$p"F][n$!3-x6)[MS(**fF/7$$"3eL$e9w,')p"F][n$!3+i_gv(H4H&F/7$$"3eLe9cS!Rq"F][n$!3g#Q#H?A!4[%F/7$$"3fLL$3N1#4<F][n$!3ugD^M>P%e$F/7$$"3D]P%)RZY9<F][n$!3\q]>_(*REEF/7$$"3#p;a)GJs><F][n$!3(=9Y6=ezh"F/7$$"3e$eky^")\s"F][n$!3..l_xrA$y&F27$$"3C+](o!*R-t"F][n$"3K!\NI98[s%F27$$"3"pT&)eH)\N<F][n$"3d3s1f+;9:F/7$$"3eLe*[oc2u"F][n$"3eELmn!Rm_#F/7$$"3C]i!R2:gu"F][n$"3%=&H#)3ea!\$F/7$$"3!pm;HYt7v"F][n$"3bDe=7[n(Q%F/7$$"39+vo*GP4w"F][n$"3yP8n!R'G3eF/7$$"3uL$ek6,1x"F][n$"3H8nNYCWkoF/7$$"3)p;HK%\E!y"F][n$"3/MR;B$e7](F/7$$"3A+++q(G**y"F][n$"3ca;5>dT(p(F/7$$"3*pmTgg/5!=F][n$"3+KURqIh*R(F/7$$"3wLL3U/37=F][n$"3PH[)QZ&p;mF/7$$"3a+]7yi:B=F][n$"3nn<:J7GsaF/7$$"3'pmmT6KU$=F][n$"3%=,d,3%4DTF/7$$"3WL$eRZQT%=F][n$"3i*GV<SBA*GF/7$$"3F++vL[/a=F][n$"3R)>9nGPJw"F/7$$"35n;a$>^R'=F][n$"35mR*oG*f.&)F27$$"3dLLL`v&Q(=F][n$"3#fY5))GS"QCF27$$"30Dcw9")\w=F][n$"3s)[9Wkp?U"F27$$"3)o"z>w'Q"z=F][n$"3v"f!H(**R#[nFey7$$"3r3-jP#z<)=F][n$"3b4@3*e\h,#Fey7$$"3>+D1*z>W)=F][n$"3I'4?QQZ8u&F[jl7$$"3n"z%\g.1()=F][n$"3g#*z=(3Ho&))F]ho7$$"3]$3F>#4q*)=F][n$"3OpcE!e&=&\%Fey7$$"3Mv$fL[TB*=F][n$"3>wp5@i2'3"F27$$"3#om"zW?)\*=F][n$"3%yAp;h-Q*>F27$$"3VL3_!HWb!>F][n$"3f(QMz*pB#=)F27$$"30++DOl5;>F][n$"3+4BRH2P)y"F/7$$"3#***\7`f@E>F][n$"3t3feD&pg%HF/7$$"39+++q`KO>F][n$"3&=nq([P<1UF/7$$"3O+](oyMk%>F][n$"3!*=m(*)4l`V&F/7$$"3A++v.Uac>F][n$"3GfPxi@a*\'F/7$$"33+D"G:3u'>F][n$"3ml>8x!)y>tF/7$$"3H+](=5s#y>F][n$"3y9ql"oMno(F/7$$"3<D19*3))4)>F][n$"3!RMM]jBup(F/7$$"3/]iSwSq$)>F][n$"3T$*QmSC%Rn(F/7$$"3#\(=nj+U')>F][n$"3A[U)>^%y:wF/7$$"3:+v$40O"*)>F][n$"3!e1Z7PhE_(F/7$$"3E](oa-oX*>F][n$"3'yKB75p9B(F/7$$"#?F+$"3BUF96_Z-oF/-%&COLORG6&%$RGBG$F+!""FijpFijp-F&6$7ctF)7$F-$"3r-w#GX,x3"F/7$F4$"3#omk:3'\i@F/7$F9$"3#4*yP;-j6KF/7$F>$"3s$p(fyYlAUF/7$FH$"3K"f*)Q**Ge&eF/7$FR$"3q!>.Ca.!zsF/7$F[p$"3nV?$RIyac)F/7$Fep$"3'>@&GI(pPY*F/7$F_q$"3k8xP6vVb(*F/7$Fiq$"36v>a"e*yM**F/7$F^r$"3&*>'eon];)**F/7$Fcr$"3]!z6a.h(****F/7$Fhr$"3K>$oG\o!*)**F/7$F]s$"3(\r)eZQg\**F/7$Fat$"3yRMhZ,p5&*F/7$F[u$"3wzy*fGr"R')F/7$Fiv$"3g)oe:=d*yuF/7$Fcw$"3))z>=f8<EgF/7$F]x$"3DqhrEXFuUF/7$Fgx$"3OHrRh4:VBF/7$F\y$"3a9'z:r32I"F/7$Fay$"3-oSm>8XOCF27$Fgz$!3vZ%ySus:;)F27$Fa[l$!3qaQA<_ym=F/7$Ff[l$!3+%H`gRsJ*GF/7$F[\l$!3LqEs``C()QF/7$F`\l$!3SA+Ef6!z$[F/7$Fe\l$!3]V"[N"=_MdF/7$F_]l$!3%H+y[bxtO(F/7$F]_l$!3)3"o\e+-`')F/7$Fg_l$!33Z^:%fz"\%*F/7$F[al$!3m-9$enX&**)*F/7$F`al$!3nNGBv!e8'**F/7$Feal$!3y'y$R\W@%***F/7$Fjal$!3-sFD!H>!)***F/7$F_bl$!3&[&[wP:ws**F/7$Fibl$!3gW(z**>Oa$)*F/7$Fccl$!3A_n7/S$Qe*F/7$F]dl$!3\PA#**['\Y()F/7$Fefl$!3)3o#Rh!>0](F/7$F_gl$!3Cf%eYj2u'fF/7$Figl$!3'e"*[ti0`<%F/7$Fchl$!3)G+o_-y')Q#F/7$F]il$!3oSGlR=0l^F27$Fbjl$"3mvMF+a6(4'F27$F\[m$"3FL*zJt%>G<F/7$Fa[m$"3#H$\+ZwvCGF/7$Ff[m$"3h2#G!o:\&)QF/7$F`\m$"3>\!3H*GOjbF/7$Fj\m$"3#>M#>Jc2RqF/7$Fh^m$"3WG&Heqw1V)F/7$Fb_m$"3mMr3]T>3%*F/7$F\`m$"3G:P(\hd`p*F/7$Ff`m$"3?^Dm([L*)))*F/7$F[am$"3s1zj6j+]**F/7$F`am$"3r^Q49K0()**F/7$Feam$"2cl5#RZ)*****Fgo7$Fjam$"3OI3qh'p())**F/7$F^cm$"3U5P@fU&fl*F/7$Fhcm$"3U?Aj$R?d())F/7$Ffem$"3X1J5fat\xF/7$F`fm$"37aYW<Y-)H'F/7$Fefm$"3u3Z)eff7V&F/7$Fjfm$"3@$>$HP]?-XF/7$F_gm$"3U/pD)*f^@NF/7$Fdgm$"3]_[?;(R/]#F/7$F^hm$"3;t$o8))\9f&F27$Fbim$!3QV-+==t.9F/7$Fgim$!3'o`vMOMYW#F/7$F\jm$!3C%GPEYG!eMF/7$Fajm$!3;o'[i"3^KWF/7$Ffjm$!3?#\VE)f6d`F/7$Fa[n$!3%ox"=;@3uqF/7$F_]n$!3cF]^Yad[%)F/7$Fi]n$!3lR9^0Z$RJ*F/7$F]_n$!3%*G!R([.FP)*F/7$Fb_n$!3fYezX"Hr"**F/7$Fg_n$!3"4SR%GEOq**F/7$F\`n$!3e0kXwy#o***F/7$Fa`n$!3K#[mk$QX'***F/7$Ff`n$!3!*z[o7:Cp**F/7$F[an$!37&QEU'RE:**F/7$F`an$!3gKw&*3hmM)*F/7$Fean$!3y^WUMVmF(*F/7$Fibn$!3"\x")eX+H,*F/7$Fgdn$!3%R\!*G&fS')yF/7$Faen$!31lx?j:FNkF/7$F[fn$!3'o-%[i*HFq%F/7$F`fn$!3qXhb$[&p&y$F/7$Fefn$!3_58Nr%3)HGF/7$Fjfn$!3p7%f#z"z[%=F/7$F_gn$!3IoeK6#f,T)F27$Fdhn$"3!3,SHmyE$GF27$F^in$"3(>N.DJoRS"F/7$Fcin$"3YQZ8Y&3p]#F/7$Fhin$"39njoij8yNF/7$Fbjn$"3#e2Qtgw2Q&F/7$F\[o$"3wu\&Hu4T'pF/7$Fj\o$"3z;lL+0%*R$)F/7$Fd]o$"3wd!3\u[%G$*F/7$F^^o$"3!=WxiXSdj*F/7$Fh^o$"3&y4KsS')3&)*F/7$F]_o$"3()>PQgnAB**F/7$Fb_o$"3CiiZv"H=(**F/7$Fg_o$"3s]fz(Qxl***F/7$F\`o$"3#QKzc>7u***F/7$Fa`o$"3JPCky7'4(**F/7$Ff`o$"32leGyF+;**F/7$F[ao$"3%3$pHCQpK)*F/7$F`ao$"3(4;I?gs7s*F/7$Fjao$"3aUGqcqW:%*F/7$Fdbo$"3XB3eP6--!*F/7$Fbdo$"3C")R4Fwt\zF/7$F\eo$"3CCy<&*=]wlF/7$Ffeo$"3#\sf(frGe[F/7$F`fo$"3LL7z'GHe#HF/7$Fefo$"3-lvN%*>mG>F/7$Fjfo$"3;O^hYB86"*F27$F_ho$!3U\V43(Q1;"F27$Fiho$!3y1#o8X9?9"F/7$F^io$!3"R'yd&[yH?#F/7$Fcio$!3F>3cj!H%QKF/7$Fhio$!3nG[$QFujB%F/7$F]jo$!3F$fgvcc_=&F/7$Fgjo$!30em?vM"[$oF/7$Fa[p$!3))[&*)QrP9>)F/7$F[\p$!3nz`&QTB`@*F/7$F_]p$!3_#RNvZGi#)*F/7$Fd]p$!3bB=_/V?5**F/7$Fi]p$!3jo=."3%ym**F/7$F^^p$!3[lIK'R6e***F/7$Fc^p$!3_D*fk+1s***F/7$Fh^p$!3mTD9cS'4(**F/7$F]_p$!3m*Hk$*3er"**F/7$Fb_p$!3G#>p)[o$f$)*F/7$Fg_p$!3$=:j\'[_F(*F/7$Fa`p$!3t6A<a03,"*F/7$F[ap$!3ui8ha\rN")F/7$Feap$!32D6)yl(QfmF/7$F_bp$!3At+rG0id[F/7$Fibp$!3qPw-uj3UIF/7$Fccp$!3M'4*e2r_26F/7$Fgdp$!3()QbRy_!zN&Fey7$F[fp$"3Y;s)*zh'4+"F/7$F`fp$"3%>%[=3\NW?F/7$Fefp$"3\B;s'zd\1$F/7$F_gp$"38<(G"y6,9\F/7$Figp$"3<(ppQfiGc'F/7$Fchp$"3M-mZ^73N!)F/7$Fajp$"3mwiF2DXH"*F/-Ffjp6&Fhjp$"#5FjjpFijpFijp-F&6$7ctF)7$F-$!3r-w#GX,x3"F/7$F4$!3#omk:3'\i@F/7$F9$!3#4*yP;-j6KF/7$F>$!3s$p(fyYlAUF/7$FH$!3K"f*)Q**Ge&eF/7$FR$!3q!>.Ca.!zsF/7$F[p$!3nV?$RIyac)F/7$Fep$!3'>@&GI(pPY*F/7$F_q$!3k8xP6vVb(*F/7$Fiq$!36v>a"e*yM**F/7$F^r$!3&*>'eon];)**F/7$Fcr$!3]!z6a.h(****F/7$Fhr$!3K>$oG\o!*)**F/7$F]s$!3(\r)eZQg\**F/7$Fat$!3yRMhZ,p5&*F/7$F[u$!3wzy*fGr"R')F/7$Fiv$!3g)oe:=d*yuF/7$Fcw$!3))z>=f8<EgF/7$F]x$!3DqhrEXFuUF/7$Fgx$!3OHrRh4:VBF/7$F\y$!3a9'z:r32I"F/7$Fay$!3-oSm>8XOCF27$Fgz$"3vZ%ySus:;)F27$Fa[l$"3qaQA<_ym=F/7$Ff[l$"3+%H`gRsJ*GF/7$F[\l$"3LqEs``C()QF/7$F`\l$"3SA+Ef6!z$[F/7$Fe\l$"3]V"[N"=_MdF/7$F_]l$"3%H+y[bxtO(F/7$F]_l$"3)3"o\e+-`')F/7$Fg_l$"33Z^:%fz"\%*F/7$F[al$"3m-9$enX&**)*F/7$F`al$"3nNGBv!e8'**F/7$Feal$"3y'y$R\W@%***F/7$Fjal$"3-sFD!H>!)***F/7$F_bl$"3&[&[wP:ws**F/7$Fibl$"3gW(z**>Oa$)*F/7$Fccl$"3A_n7/S$Qe*F/7$F]dl$"3\PA#**['\Y()F/7$Fefl$"3)3o#Rh!>0](F/7$F_gl$"3Cf%eYj2u'fF/7$Figl$"3'e"*[ti0`<%F/7$Fchl$"3)G+o_-y')Q#F/7$F]il$"3oSGlR=0l^F27$Fbjl$!3mvMF+a6(4'F27$F\[m$!3FL*zJt%>G<F/7$Fa[m$!3#H$\+ZwvCGF/7$Ff[m$!3h2#G!o:\&)QF/7$F`\m$!3>\!3H*GOjbF/7$Fj\m$!3#>M#>Jc2RqF/7$Fh^m$!3WG&Heqw1V)F/7$Fb_m$!3mMr3]T>3%*F/7$F\`m$!3G:P(\hd`p*F/7$Ff`m$!3?^Dm([L*)))*F/7$F[am$!3s1zj6j+]**F/7$F`am$!3r^Q49K0()**F/7$Feam$!2cl5#RZ)*****Fgo7$Fjam$!3OI3qh'p())**F/7$F^cm$!3U5P@fU&fl*F/7$Fhcm$!3U?Aj$R?d())F/7$Ffem$!3X1J5fat\xF/7$F`fm$!37aYW<Y-)H'F/7$Fefm$!3u3Z)eff7V&F/7$Fjfm$!3@$>$HP]?-XF/7$F_gm$!3U/pD)*f^@NF/7$Fdgm$!3]_[?;(R/]#F/7$F^hm$!3;t$o8))\9f&F27$Fbim$"3QV-+==t.9F/7$Fgim$"3'o`vMOMYW#F/7$F\jm$"3C%GPEYG!eMF/7$Fajm$"3;o'[i"3^KWF/7$Ffjm$"3?#\VE)f6d`F/7$Fa[n$"3%ox"=;@3uqF/7$F_]n$"3cF]^Yad[%)F/7$Fi]n$"3lR9^0Z$RJ*F/7$F]_n$"3%*G!R([.FP)*F/7$Fb_n$"3fYezX"Hr"**F/7$Fg_n$"3"4SR%GEOq**F/7$F\`n$"3e0kXwy#o***F/7$Fa`n$"3K#[mk$QX'***F/7$Ff`n$"3!*z[o7:Cp**F/7$F[an$"37&QEU'RE:**F/7$F`an$"3gKw&*3hmM)*F/7$Fean$"3y^WUMVmF(*F/7$Fibn$"3"\x")eX+H,*F/7$Fgdn$"3%R\!*G&fS')yF/7$Faen$"31lx?j:FNkF/7$F[fn$"3'o-%[i*HFq%F/7$F`fn$"3qXhb$[&p&y$F/7$Fefn$"3_58Nr%3)HGF/7$Fjfn$"3p7%f#z"z[%=F/7$F_gn$"3IoeK6#f,T)F27$Fdhn$!3!3,SHmyE$GF27$F^in$!3(>N.DJoRS"F/7$Fcin$!3YQZ8Y&3p]#F/7$Fhin$!39njoij8yNF/7$Fbjn$!3#e2Qtgw2Q&F/7$F\[o$!3wu\&Hu4T'pF/7$Fj\o$!3z;lL+0%*R$)F/7$Fd]o$!3wd!3\u[%G$*F/7$F^^o$!3!=WxiXSdj*F/7$Fh^o$!3&y4KsS')3&)*F/7$F]_o$!3()>PQgnAB**F/7$Fb_o$!3CiiZv"H=(**F/7$Fg_o$!3s]fz(Qxl***F/7$F\`o$!3#QKzc>7u***F/7$Fa`o$!3JPCky7'4(**F/7$Ff`o$!32leGyF+;**F/7$F[ao$!3%3$pHCQpK)*F/7$F`ao$!3(4;I?gs7s*F/7$Fjao$!3aUGqcqW:%*F/7$Fdbo$!3XB3eP6--!*F/7$Fbdo$!3C")R4Fwt\zF/7$F\eo$!3CCy<&*=]wlF/7$Ffeo$!3#\sf(frGe[F/7$F`fo$!3LL7z'GHe#HF/7$Fefo$!3-lvN%*>mG>F/7$Fjfo$!3;O^hYB86"*F27$F_ho$"3U\V43(Q1;"F27$Fiho$"3y1#o8X9?9"F/7$F^io$"3"R'yd&[yH?#F/7$Fcio$"3F>3cj!H%QKF/7$Fhio$"3nG[$QFujB%F/7$F]jo$"3F$fgvcc_=&F/7$Fgjo$"30em?vM"[$oF/7$Fa[p$"3))[&*)QrP9>)F/7$F[\p$"3nz`&QTB`@*F/7$F_]p$"3_#RNvZGi#)*F/7$Fd]p$"3bB=_/V?5**F/7$Fi]p$"3jo=."3%ym**F/7$F^^p$"3[lIK'R6e***F/7$Fc^p$"3_D*fk+1s***F/7$Fh^p$"3mTD9cS'4(**F/7$F]_p$"3m*Hk$*3er"**F/7$Fb_p$"3G#>p)[o$f$)*F/7$Fg_p$"3$=:j\'[_F(*F/7$Fa`p$"3t6A<a03,"*F/7$F[ap$"3ui8ha\rN")F/7$Feap$"32D6)yl(QfmF/7$F_bp$"3At+rG0id[F/7$Fibp$"3qPw-uj3UIF/7$Fccp$"3M'4*e2r_26F/7$Fgdp$"3()QbRy_!zN&Fey7$F[fp$!3Y;s)*zh'4+"F/7$F`fp$!3%>%[=3\NW?F/7$Fefp$!3\B;s'zd\1$F/7$F_gp$!38<(G"y6,9\F/7$Figp$!3<(ppQfiGc'F/7$Fchp$!3M-mZ^73N!)F/7$Fajp$!3mwiF2DXH"*F/F`gr-%+AXESLABELSG6$Q"t6"Q!F]dt-%%VIEWG6$;FijpFajp;$!2#3z(GT)**R5F][n$"2#3z(GT)**R5F][n

omega:=2:plot([sol(t),env(t),-env(t)],t=0..20,color=[black,red,red]);

-%%PLOTG6'-%'CURVESG6$7]]l7$$""!F+F*7$$"3dmmm;arz@!#=$"3JO.N]p3@!*!#>7$$"39LLLL3VfVF/$"3XmHhRe\nIF/7$$"3\****\i&*)fD'F/$"3Ak^<'zhM#\F/7$$"3%pmm;H[D:)F/$"3K95UK>wicF/7$$"3#QL$e9w)*=#*F/$"3-,a7*))\WG&F/7$$"3'****\PpU&G5!#<$"38*p'3k")o[UF/7$$"3am;/Em=N6FJ$"3Yr4>$[Z<d#F/7$$"3MLLLe0$=C"FJ$"3CYw%3?j[W$F27$$"3ELL3xf]&H"FJ$!3%f*fbNNem$*F27$$"3SLL$eR"=\8FJ$!3m&GYW%QZ"H#F/7$$"3cLLe9o&GS"FJ$!3;P1#)eEy!p$F/7$$"3[LLLLA`c9FJ$!3"*)fUEDhI5&F/7$$"3bLL$32$)Qc"FJ$!3)ykOP2HL$yF/7$$"3iLLL3RBr;FJ$!3G**==>JL@5FJ7$$"3#omTg_u!y<FJ$!3kZD1EzD)>"FJ7$$"3B++vV^"\)=FJ$!3'[,PT;3WH"FJ7$$"3g$3x")HD;">FJ$!3Yx!p&z)[RI"FJ7$$"3&p;/EXN$Q>FJ$!3FU8!>&eL28FJ7$$"34]7.2c/l>FJ$!3C0FV_#[WI"FJ7$$"3WL$e9wb<*>FJ$!3=rA[%[*>&H"FJ7$$"3#**\7.2w^/#FJ$!3y]CpT"[uD"FJ7$$"3imm;zjf)4#FJ$!3UTmOY45%>"FJ7$$"3aLLL38l(>#FJ$!3+3Lm0HO65FJ7$$"3-++]Piq'H#FJ$!3")pt3"Rv2_(F/7$$"3[LL3-PBYBFJ$!3fp9xoeq#)fF/7$$"3[mmmm6w&R#FJ$!3d9dq\*\ZJ%F/7$$"3&****\7j)GXCFJ$!3L_Ly7y(Ra#F/7$$"3ULL$e4;[\#FJ$!3I!z/:]6!)*pF27$$"3wmmm;*)4YDFJ$"3U_-bf;"QD"F/7$$"37++]P<Q(f#FJ$"3sZpV@hp;KF/7$$"3ZLLLeXm[EFJ$"3rEXH()QD_^F/7$$"3#omm"zt%**p#FJ$"3g1Z,&p?S-(F/7$$"3=++++-B^FFJ$"3IS$pzVIkz)F/7$$"3`LL$3-8D!GFJ$"3![\)eTkbV5FJ7$$"3)omm;%ez`GFJ$"394oM-p)4>"FJ7$$"3!)****\i'y]!HFJ$"3s=B8!e#3>8FJ7$$"3gLL$e>_6,$FJ$"3y")4&\@bC^"FJ7$$"3'pmm"HdA<JFJ$"3%4,]_l8pf"FJ7$$"3I++]7TuVJFJ$"3#e(pVIf(**f"FJ7$$"3jLL$e\i-<$FJ$"3#*enw#*zs&f"FJ7$$"3'pmm"z3y'>$FJ$"3j*4#)*>@>%e"FJ7$$"3K++]i#*HBKFJ$"3[%3w%*zGac"FJ7$$"3*pmm"HgLwKFJ$"3I"RK1^]m]"FJ7$$"3oLL$ezs$HLFJ$"3&p*o@1Ei?9FJ7$$"3#pm;HZRAQ$FJ$"3!\l7$*GP&48FJ7$$"3=+++]h5NMFJ$"3#GdfeVga<"FJ7$$"3XLL3FG(z[$FJ$"3t0A`Vy:@5FJ7$$"3qmm;/&R3a$FJ$"3!pauVa$*z\)F/7$$"3'****\7=1Pf$FJ$"3x(GK#Q9()[mF/7$$"3ALLLeGdYOFJ$"3$Q!))3ntw,ZF/7$$"3YmmTN&R%*p$FJ$"3QP$*G`j#fp#F/7$$"3=++]7iI_PFJ$"3O:Y1sk09nF27$$"3IL3-)3'o1QFJ$!3:N`t+$[%)Q"F/7$$"3'omTN'f1hQFJ$!3WLJ,AVL$Q$F/7$$"3V+D1ReW:RFJ$!3C#fk4$G(GF&F/7$$"3+MLe9d#)pRFJ$!3$GL"3#)\m>qF/7$$"3omT5!f0U-%FJ$!3Y-eh3[8!f)F/7$$"3B+]ilaeySFJ$!3ma;Ni%p_&**F/7$$"3!Q$e9T`'H8%FJ$!3s$4-'oR746FJ7$$"3Onmm;_M(=%FJ$!3gV$p8e))z>"FJ7$$"3z+]iSICNUFJ$!3ut)Qed$za7FJ7$$"3?MLek39$G%FJ$!39>-P0r-"H"FJ7$$"3#4]ilx*32VFJ$!3u1Q5ksR,8FJ7$$"3in;a)oQ5L%FJ$!3Bh"=;VKmI"FJ7$$"3LM3_+w)\N%FJ$!3$H#)z#RLy18FJ7$$"3/,+]7l$*yVFJ$!3e9Wq\J#>I"FJ7$$"3)ym;/;KZZ%FJ$!3,Af,^ieM7FJ7$$"3$QLL$3y_qXFJ$!3/oSFFzH)4"FJ7$$"3$4+](=5PyYFJ$!3s@h1Bi]'z)F/7$$"3;nm;HU@'y%FJ$!3lR55M"*fbhF/7$$"3G+]PMe8S[FJ$!3/SJUUe))[ZF/7$$"3QLLeRu0%*[FJ$!3_H5"oKZ.L$F/7$$"3Rn;zW!zz%\FJ$!3\ums@v@L>F/7$$"3]+++]1!>+&FJ$!3IDq&=fA"*)eF27$$"3Y+++vm=5^FJ$"3T;NHG17Q=F/7$$"3S++++FZ=_FJ$"32=?QEkw[PF/7$$"3O+++D(enK&FJ$"3.IvvBt!=-&F/7$$"3J+++]Z/NaFJ$"3z[+cf<>9cF/7$$"3_*****\d@s[&FJ$"3X$3/b#*\Um&F/7$$"3h*******R)RRbFJ$"3[lC+4G^tbF/7$$"3q*****\Av:f&FJ$"3FPi[(z=bN&F/7$$"3!)******\?vVcFJ$"3;58sU(>o-&F/7$$"3)********p0"[dFJ$"3j_#HK'>O:TF/7$$"3;+++]$fC&eFJ$"3x9;i80Z5IF/7$$"3Qnm"Hd&)>/'FJ$"3'R"o/ARl"4"F/7$$"3qLL$ez6:B'FJ$"3cg.z.*p[K&!#?7$$"3P+vV[I&yG'FJ$"3<I8SP)euN%!#A7$$"3/n;/,V>WjFJ$"3c$eAJs:UT(Fgfl7$$"3rLek`b`+kFJ$"3#onS_M>Lr#F27$$"3P++D1o(oX'FJ$"3Oe2_VhcQeF27$$"3rL$e9Jf&plFJ$"3g/z\O$)\)\"F/7$$"3/nmm;=C#o'FJ$"3SIXpnv^kEF/7$$"3knmmTb:toFJ$"3e_7$o>\-j%F/7$$"3Mnmmm#pS1(FJ$"3NT@efb&>l&F/7$$"3!3DcE-H=4(FJ$"3\^;;y,[lcF/7$$"3GMeky()e>rFJ$"3/m]L&e.$QcF/7$$"3v<ajM&[t9(FJ$"3aTF&*p"4*obF/7$$"3K+]i!H3^<(FJ$"3.l6n:E3caF/7$$"3QmTg-yiIsFJ$"3O\j*4"p'o4&F/7$$"3JLLe9t9'G(FJ$"3)f5&Rn&\ub%F/7$$"3=n;aQj=(R(FJ$"3o$*>'>^BE&HF/7$$"3<++]i`A3vFJ$"32CP!\,())esF27$$"3Gm;a8P^1wFJ$!3shL*H(\]J;F/7$$"3GLLek?![q(FJ$!3&)zlqPsd%=%F/7$$"3G+]i:/4.yFJ$!3smrI!GZ>u'F/7$$"3Rmmmm(y8!zFJ$!390*[*y\y(4*F/7$$"3y+]ilm@4!)FJ$!38"zW%*Q%*47"FJ7$$"3IMLekX0<")FJ$!3D4qH2=kf7FJ7$$"3c=HKRS,W")FJ$!3`1l*4+b1G"FJ7$$"3/,D19N(4<)FJ$!3_9$>yPDdH"FJ7$$"3a$3-)))H$z>)FJ$!3YG@&[2lYI"FJ7$$"3!ymTNY#*[A)FJ$!3XWaT2&>tI"FJ7$$"3cM3-89")y#)FJ$!3?BU'\;GLH"FJ7$$"3K,+]i.tK$)FJ$!3ma5:ASA`7FJ7$$"3u++vVvTN%)FJ$!3_-MJ%p^`5"FJ7$$"3<+++DZ5Q&)FJ$!3%eqQas$[*p)F/7$$"3x+]i:$[%*e)FJ$!3C5_[7SGNsF/7$$"3Q,+D1>zS')FJ$!32-okmbC5cF/7$$"3=+](o\N@p)FJ$!3Eb-pjt1_QF/7$$"3!3++v3zMu)FJ$!3;--(>2/;*>F/7$$"3EM3-Q20(z)FJ$"3O$HtYO%o\AFgfl7$$"3rn;a)QA1&))FJ$"3?b0'3i5:2#F/7$$"3=,D1RS>/*)FJ$"3yTw:!edS6%F/7$$"3jMLe*olx&*)FJ$"3>+*R5c'Q3hF/7$$"34oT5StL6!*FJ$"380m0ygK8!)F/7$$"3b,]i!**3\1*FJ$"3"HpU69G#*y*F/7$$"3,Ne9T1[="*FJ$"3_%H-g<)))R6FJ7$$"3Yomm"H_?<*FJ$"3%ed9JQP3G"FJ7$$"3@n;a)GV/F*FJ$"3m/q'oyizZ"FJ7$$"3tnmT&GM)o$*FJ$"3.1kWIsv$e"FJ7$$"3)pTNY.KMR*FJ$"3I%R/>x$*[f"FJ7$$"3+oT&QyH!=%*FJ$"3A["o'4Kw*f"FJ7$$"3->H2LviU%*FJ$"3EFceqNM)f"FJ7$$"3Fo;H#GDsY*FJ$"3_0q(4ET1f"FJ7$$"3vm"H2y?k^*FJ$"3:oqjAebc:FJ7$$"3,nm;zihl&*FJ$"3=&R;`.@")\"FJ7$$"3&*)\7.F!o='*FJ$"3f*y)>')R,49FJ7$$"3lK$e9EW<n*FJ$"3%[G$f=*pYH"FJ7$$"3OmTg_#3[s*FJ$"3)4W1'[@Zd6FJ7$$"33++vVA(yx*FJ$"3"o*[#)z1F+5FJ7$$"3zLe*[BO4$)*FJ$"3X'p%y?5<j#)F/7$$"3\n;/E-+%))*FJ$"3')Rie!30>R'F/7$$"3@,v=<U1P**FJ$"3rw+3'4irU%F/7$$"39LLL3#G,***FJ$"3G/Y5a?z3CF/7$$"3<$3x"yY_/5!#;$"3F"e)y3.!)*)HF27$$"3@L3_Nl.55F^im$!3=8HXhavz<F/7$$"3D$ekGR[b,"F^im$!3*Q9u9"4b$y$F/7$$"3HL$3-Dg5-"F^im$!3`u)=(Qv!4n&F/7$$"3K$3_v5sl-"F^im$!3=vx"ecjOS(F/7$$"3OLe*['R3K5F^im$!3L#o!f2N(y%*)F/7$$"3S$eRA#efP5F^im$!3!>Ex`Cdu-"FJ7$$"3WLLezw5V5F^im$!3c?!GfkSg8"FJ7$$"3<+]ibQq_5F^im$!3*f$*\I=IGE"FJ7$$"3tmmmJ+Ii5F^im$!3"4o!*HausI"FJ7$$"3HL$3x?'*=2"F^im$!3.Wk%)pY#4F"FJ7$$"3.++v$Q#\"3"F^im$!3*fN;!or*4;"FJ7$$"3OL3x;l&=4"F^im$!3wZ%*3>E7P(*F/7$$"3nm;z\1A-6F^im$!3XHj5Z5;]tF/7$$"3++D"Gy%e76F^im$!3$GN>s@:Co%F/7$$"3]LL$e"*[H7"F^im$!3m&oM/2%)f(>F/7$$"37+]PzglL6F^im$"3^s+Fk(3e='F27$$"3wmm"HCjV9"F^im$"3ktE92yE)z#F/7$$"3RL$ekSq]:"F^im$"3$)Q=qxJ!)3WF/7$$"3-+++qvxl6F^im$"3[:DJF%eqO&F/7$$"3,]il(G'Ro6F^im$"3sr2$\76(*\&F/7$$"3=+DJ0],r6F^im$"3SmBN-F:$f&F/7$$"3<](oHsLO<"F^im$"3Z2UK4?A[cF/7$$"3;+]iSCDw6F^im$"3<yBB;_+mcF/7$$"3:]7Ge6()y6F^im$"3TDTS._#yk&F/7$$"3:+v$f()*["="F^im$"3oG)G=ZH_f&F/7$$"39]Pf$f3T="F^im$"3D<zkgm(*4bF/7$$"38++D6ts'="F^im$"3'*e!z`w@SR&F/7$$"35+](==-s>"F^im$"3)\%pKp$H#oYF/7$$"31++]_qn27F^im$"3ji-^=&Qpk$F/7$$"33+]P/q%zA"F^im$"3'y1r&y_].:F/7$$"36++Dcp@[7F^im$"3FOxUn))429F27$$"31DJ&pCI5D"F^im$"3DaSp!p%)eE'Fgfl7$$"3,]ilPN%QD"F^im$"35=BK'*eVf:Fgfl7$$"3'\Pf$Golc7F^im$"3D25')G\i9y!#D7$$"33+D1>,Zf7F^im$"3)fw&\:x%Qg"Fgfl7$$"3;](o/q'4l7F^im$"3N.<Pe+C?9F27$$"31+](=GB2F"F^im$"37X<$GH.P)QF27$$"3.+voWk(>G"F^im$"3YEygOyx'>"F/7$$"3+++]2'HKH"F^im$"3g(ep;!o*oI#F/7$$"3ELL3UDX88F^im$"3&o!39A@sLWF/7$$"3_mmmwanL8F^im$"3MXN@c\fOcF/7$$"3%**\iS^ujL"F^im$"3'y!GLO=![m&F/7$$"3=L$e9bt!R8F^im$"3F,!Q'*Q">bcF/7$$"3UmT&))es<M"F^im$"3x.!4^5dig&F/7$$"3$)***\iirWM"F^im$"3`8cUanv;bF/7$$"3mm;/,(p)\8F^im$"3]-?UlY[7_F/7$$"3JLL$exn_N"F^im$"3!fjHqVe"QZF/7$$"3zmmTDR1m8F^im$"3qS$f!**p!oG$F/7$$"35+++v+'oP"F^im$"3#>D$Ga)GqA"F/7$$"3HLe9"*Hk'Q"F^im$!37@sr,&>"\5F/7$$"3om;H2fU'R"F^im$!3PL_ocw@gNF/7$$"3/+vVB)3iS"F^im$!31XHzR")GBhF/7$$"3CLLeR<*fT"F^im$!3s'ys&*>2t`)F/7$$"3***\P40(oE9F^im$!3g">\cPEn2"FJ7$$"3um;HiBQP9F^im$!3=+;U*4*\L7FJ7$$"36](oz,IFW"F^im$!3Xqt2mDs!G"FJ7$$"3\Lektw2[9F^im$!3FyJmM3f/8FJ7$$"33vV[,:v]9F^im$!3B))=g)>HtI"FJ7$$"3'o"HKH`U`9F^im$!3e)fa(>!pPI"FJ7$$"3ke9;d"*4c9F^im$!3K_v-6r#QH"FJ7$$"3B+++&)Hxe9F^im$!3.^;++cXx7FJ7$$"3ym"z%Rk$)o9F^im$!3KTJrjyUe6FJ7$$"3KL$eR*)**)y9F^im$!3cm/E**>-F&*F/7$$"3p;z>@;$R["F^im$!3NNdX_qK0#)F/7$$"30+vV[L'*)["F^im$!3D"yn6aaPr'F/7$$"3S$3xc2&*R\"F^im$!32mY1_n8w]F/7$$"3gmm"H!o-*\"F^im$!3T;7p]-c>LF/7$$"3LL$3xS'G/:F^im$!35c@_VOm)Q"F/7$$"3*)****\7ga4:F^im$"3Pe'G+)*H-.'F27$$"3jm;H<c![^"F^im$"3)HaLS%*>rh#F/7$$"3PLL3A_1?:F^im$"31a;&oGxUh%F/7$$"35+](o#[KD:F^im$"3"orATTM]b'F/7$$"3%omm;V%eI:F^im$"3)Q;R$4")o+%)F/7$$"3SL$ek.We`"F^im$"3MxoF&*[T65FJ7$$"39++DTO5T:F^im$"3e(p?3fwg;"FJ7$$"3vmTN"4)Q^:F^im$"3nO<Q#[n'39FJ7$$"3OL$e9as;c"F^im$"30&=en%p$pb"FJ7$$"3-vV)RlVUc"F^im$"3*)QC7I?tx:FJ7$$"3n;/^mZ"oc"F^im$"3#R!*[Ylk<f"FJ7$$"3Kek.zeQp:F^im$"3K$4d#fc'*)f"FJ7$$"3(**\i:*p&>d"F^im$"3'\tqWa*H*f"FJ7$$"3G$e9m@*4x:F^im$"3d#)QWMKRz:FJ7$$"3emmmT9C#e"F^im$"3w)=ZknPC`"FJ7$$"3y*\7yI3If"F^im$"3tQ'f+%>@^8FJ7$$"3;L$eR<vPg"F^im$"3$33g*eudr5FJ7$$"3%)\7.2'e"4;F^im$"3Q*4aV4g,-*F/7$$"3`mT5S?a9;F^im$"3/4Q(o2mH<(F/7$$"3A$3xJZD*>;F^im$"3%4i#f-n;8_F/7$$"3"****\i!*3`i"F^im$"3irT)[*)3==$F/7$$"3q;a8#z$\I;F^im$"3MIxmG64(>"F/7$$"39L3-y'ycj"F^im$!3.,6U!3f2x(F27$$"3#*\i!Rcj3k"F^im$!3SZO(*Hcb.FF/7$$"3rm;z\%[gk"F^im$!3@F[SdOnYXF/7$$"3]$3xcLL7l"F^im$!3$**eCMsiHF'F/7$$"3H+Dc@#=kl"F^im$!3yh6>,A&=&yF/7$$"3t;zW2Jgh;F^im$!30bzwvoGc#*F/7$$"3_LLL$*zym;F^im$!3+q8BIhKY5FJ7$$"3aL$3Fe#Rx;F^im$!3r4OypkWC7FJ7$$"3bLL3sr*zo"F^im$!3*3TH`<FLI"FJ7$$"3Q$3F%>$[1p"F^im$!3*)R\^!Q%G28FJ7$$"3cL3xm%*H$p"F^im$!3***>BCNU]I"FJ7$$"3u$e9Th]fp"F^im$!3[*4l\D8nH"FJ7$$"3eL$e9w,')p"F^im$!3Aw^fa;W#G"FJ7$$"3eLe9cS!Rq"F^im$!3)4LA+,/oB"FJ7$$"3fLL$3N1#4<F^im$!3(*)>Lm.&))p6FJ7$$"3#p;a)GJs><F^im$!3)G&G[IX6J)*F/7$$"3C+](o!*R-t"F^im$!3#**p(eX&)=CuF/7$$"3eLe*[oc2u"F^im$!3jz**>yB*4s%F/7$$"3!pm;HYt7v"F^im$!3A#37vDZW(>F/7$$"39+vo*GP4w"F^im$"35'eQGAhN#QF27$$"3uL$ek6,1x"F^im$"3pc8+OJR:CF/7$$"3)p;HK%\E!y"F^im$"3?bBP+2./SF/7$$"3A+++q(G**y"F^im$"3S5"f]voP2&F/7$$"3gL3-)omaz"F^im$"3U?'Q,')=9W&F/7$$"3*pmTgg/5!=F^im$"3qnYLE5mKcF/7$$"3o$3_]ctP!=F^im$"3O'H:IvjWm&F/7$$"3Q+D1CDa1=F^im$"3IivD8KebcF/7$$"32<H2$[6$4=F^im$"3K\wq&)ox2cF/7$$"3wLL3U/37=F^im$"3[r!H2YqI_&F/7$$"3a+]7yi:B=F^im$"3`eL'H9DS'[F/7$$"3'pmmT6KU$=F^im$"39$R\=[&)>$QF/7$$"3F++vL[/a=F^im$"32]h-**)*[><F/7$$"3dLLL`v&Q(=F^im$"3!f>!*ez)fICF27$$"30Dcw9")\w=F^im$"3?@Wzy*>&>9F27$$"3)o"z>w'Q"z=F^im$"3SYrO$[CDu'Fgfl7$$"3r3-jP#z<)=F^im$"3M^w0m3k:?Fgfl7$$"3>+D1*z>W)=F^im$"3'3li&yhITdF]gl7$$"3n"z%\g.1()=F^im$"3)HF')H-[e&))!#@7$$"3]$3F>#4q*)=F^im$"3emn%p!Hl#\%Fgfl7$$"3Mv$fL[TB*=F^im$"3#z1#3y?f%3"F27$$"3#om"zW?)\*=F^im$"3'>!>fdJx))>F27$$"3VL3_!HWb!>F^im$"3m_fi=p:%4)F27$$"30++DOl5;>F^im$"3sfjZACQV<F/7$$"39+++q`KO>F^im$"3W(G&3r+"))*QF/7$$"3A++v.Uac>F^im$"3enb.e]yraF/7$$"3XDc,">g#f>F^im$"3srYA1@FrbF/7$$"3L]7Gyh(>'>F^im$"3#HOM;n'GOcF/7$$"3?voal@pk>F^im$"3F2Mh;()zkcF/7$$"33+D"G:3u'>F^im$"3mn.*[w<]l&F/7$$"3=]PMF,%G(>F^im$"3u#4))3p5Z^&F/7$$"3H+](=5s#y>F^im$"3A"oE*z-U1_F/7$$"3:+v$40O"*)>F^im$"3J^:_58"R2%F/7$$"#?F+$"3KbJ5]$*z$G#F/-%&COLORG6&%$RGBG$F+!""FbfpFbfp-F&6$7bpF)7$F-$"3YkT_CBKS<F/7$F4$"3DnM]IP**fMF/7$F9$"3?P**=$fvN#\F/7$F>$"3y6&**)ph"HM'F/7$FS$"3;y*H))[x%3$*F/7$F[p$"3Z/9QInt'="FJ7$Fcr$"3%[<M$)4=tQ"FJ7$Fat$"3`uFK6E1<:FJ7$Feu$"3203`_"[6c"FJ7$Fiv$"3)fS"[e_#))e"FJ7$F^w$"3w\pZj#)f'f"FJ7$Fcw$"39Ax1_7))*f"FJ7$Fgx$"3WUTq"*\m)f"FJ7$Fay$"3??9!G!H&Hf"FJ7$Fez$"3DO7^:hAo:FJ7$Fi[l$"34x>[0O)f_"FJ7$F]]l$"3!>C<4ZbZY"FJ7$Fa^l$"3$)H@gz#=iQ"FJ7$Fi`l$"3)es\&>vq37FJ7$Fgbl$"3gM#oYVoLc*F/7$Facl$"3"fV06aR57)F/7$F[dl$"37Iv<jud$e'F/7$F_el$"33/\(*))4wG]F/7$Fiel$"3)H7N?dK#>MF/7$F^fl$"3v7%GP#Q#\#>F/7$Fcfl$"3mZsl-5ULTF27$Figl$!3"[mfn'fy(Q"F/7$Fchl$!3m(*)[6Z68<$F/7$Fhhl$!3`&)3"Qw4;l%F/7$F]il$!3[`ir/Zb*3'F/7$Fe[m$!33g.L$z)*))>*F/7$Fi\m$!3n50*3_iy:"FJ7$Fa_m$!3=[zvQPNn8FJ7$F_am$!3AO]z?113:FJ7$Fcbm$!3c!p[quxlb"FJ7$Fgcm$!3c'3Nd$HC(e"FJ7$F\dm$!3Q;\HD&Q_f"FJ7$Fadm$!3k)**[=5u$*f"FJ7$Feem$!3W`b]e'R'*f"FJ7$F_fm$!3-^Zp_X.'f"FJ7$Fcgm$!3lRE([eH^d"FJ7$Fghm$!3/!*=tV.]O:FJ7$F\jm$!3yva@%ow!y9FJ7$F`[n$!3vc_V"G4<S"FJ7$Fd\n$!3oJ6t&=6)G7FJ7$Fh]n$!3#QPxKm3i"**F/7$Fb^n$!3'yHEosIv^)F/7$F\_n$!3VVV6<#)H@qF/7$Fdan$!3]u(>R5#ezaF/7$F^bn$!3MA*RJP(zxQF/7$Fcbn$!34x4dz3M(G#F/7$Fhbn$!3KPg([U%4MnF27$Fgdn$"30:o,'>mf7"F/7$Faen$"3V!4v8N)46HF/7$Ffen$"3!H4^k@^V[%F/7$F[fn$"3)om\6L%z6gF/7$Fchn$"3Lb!Hx$))**[!*F/7$Fgin$"3p!y]k(p;W6FJ7$F_\o$"3hi]nx*3bN"FJ7$F]^o$"3_86&)\M3)\"FJ7$Fa_o$"3DD@U%\-)[:FJ7$Fe`o$"31uc!HD*R#e"FJ7$Fj`o$"3CBi1=BZ#f"FJ7$F_ao$"3Ey1`>aL)f"FJ7$Fcbo$"37h:AdI(**f"FJ7$F]co$"3C]Ix,4Q(f"FJ7$Fbco$"3+65:'pU,f"FJ7$Fgco$"3l&\[\:(Hy:FJ7$Fado$"3kOZ&)*fy=c"FJ7$F[eo$"3"R%3d-Y$4a"FJ7$F_fo$"3yL6YYA2)["FJ7$Fcgo$"3r]p'4mA#>9FJ7$F[jo$"3&e<dy1.>B"FJ7$F_[p$"3,6@gK4$e"**F/7$Fi[p$"3&G0o1)Q(zl)F/7$Fc\p$"3a_2v3LK>tF/7$Fa^p$"3t2>fwv&=q&F/7$F[_p$"3z3EBri^9SF/7$F`_p$"3)Q<9\gFIY#F/7$Fe_p$"364B"QSvQ())F27$F^bp$!3dmsSwE!y,)F27$Fhbp$!3#=eSYk6?[#F/7$F]cp$!3tt]ff_akSF/7$Fbcp$!3&e@zAYubg&F/7$Fjep$!3h;*HUxPVq)F/-F_fp6&Fafp$"#5FcfpFbfpFbfp-F&6$7bpF)7$F-$!3YkT_CBKS<F/7$F4$!3DnM]IP**fMF/7$F9$!3?P**=$fvN#\F/7$F>$!3y6&**)ph"HM'F/7$FS$!3;y*H))[x%3$*F/7$F[p$!3Z/9QInt'="FJ7$Fcr$!3%[<M$)4=tQ"FJ7$Fat$!3`uFK6E1<:FJ7$Feu$!3203`_"[6c"FJ7$Fiv$!3)fS"[e_#))e"FJ7$F^w$!3w\pZj#)f'f"FJ7$Fcw$!39Ax1_7))*f"FJ7$Fgx$!3WUTq"*\m)f"FJ7$Fay$!3??9!G!H&Hf"FJ7$Fez$!3DO7^:hAo:FJ7$Fi[l$!34x>[0O)f_"FJ7$F]]l$!3!>C<4ZbZY"FJ7$Fa^l$!3$)H@gz#=iQ"FJ7$Fi`l$!3)es\&>vq37FJ7$Fgbl$!3gM#oYVoLc*F/7$Facl$!3"fV06aR57)F/7$F[dl$!37Iv<jud$e'F/7$F_el$!33/\(*))4wG]F/7$Fiel$!3)H7N?dK#>MF/7$F^fl$!3v7%GP#Q#\#>F/7$Fcfl$!3mZsl-5ULTF27$Figl$"3"[mfn'fy(Q"F/7$Fchl$"3m(*)[6Z68<$F/7$Fhhl$"3`&)3"Qw4;l%F/7$F]il$"3[`ir/Zb*3'F/7$Fe[m$"33g.L$z)*))>*F/7$Fi\m$"3n50*3_iy:"FJ7$Fa_m$"3=[zvQPNn8FJ7$F_am$"3AO]z?113:FJ7$Fcbm$"3c!p[quxlb"FJ7$Fgcm$"3c'3Nd$HC(e"FJ7$F\dm$"3Q;\HD&Q_f"FJ7$Fadm$"3k)**[=5u$*f"FJ7$Feem$"3W`b]e'R'*f"FJ7$F_fm$"3-^Zp_X.'f"FJ7$Fcgm$"3lRE([eH^d"FJ7$Fghm$"3/!*=tV.]O:FJ7$F\jm$"3yva@%ow!y9FJ7$F`[n$"3vc_V"G4<S"FJ7$Fd\n$"3oJ6t&=6)G7FJ7$Fh]n$"3#QPxKm3i"**F/7$Fb^n$"3'yHEosIv^)F/7$F\_n$"3VVV6<#)H@qF/7$Fdan$"3]u(>R5#ezaF/7$F^bn$"3MA*RJP(zxQF/7$Fcbn$"34x4dz3M(G#F/7$Fhbn$"3KPg([U%4MnF27$Fgdn$!30:o,'>mf7"F/7$Faen$!3V!4v8N)46HF/7$Ffen$!3!H4^k@^V[%F/7$F[fn$!3)om\6L%z6gF/7$Fchn$!3Lb!Hx$))**[!*F/7$Fgin$!3p!y]k(p;W6FJ7$F_\o$!3hi]nx*3bN"FJ7$F]^o$!3_86&)\M3)\"FJ7$Fa_o$!3DD@U%\-)[:FJ7$Fe`o$!31uc!HD*R#e"FJ7$Fj`o$!3CBi1=BZ#f"FJ7$F_ao$!3Ey1`>aL)f"FJ7$Fcbo$!37h:AdI(**f"FJ7$F]co$!3C]Ix,4Q(f"FJ7$Fbco$!3+65:'pU,f"FJ7$Fgco$!3l&\[\:(Hy:FJ7$Fado$!3kOZ&)*fy=c"FJ7$F[eo$!3"R%3d-Y$4a"FJ7$F_fo$!3yL6YYA2)["FJ7$Fcgo$!3r]p'4mA#>9FJ7$F[jo$!3&e<dy1.>B"FJ7$F_[p$!3,6@gK4$e"**F/7$Fi[p$!3&G0o1)Q(zl)F/7$Fc\p$!3a_2v3LK>tF/7$Fa^p$!3t2>fwv&=q&F/7$F[_p$!3z3EBri^9SF/7$F`_p$!3)Q<9\gFIY#F/7$Fe_p$!364B"QSvQ())F27$F^bp$"3dmsSwE!y,)F27$Fhbp$"3#=eSYk6?[#F/7$F]cp$"3tt]ff_akSF/7$Fbcp$"3&e@zAYubg&F/7$Fjep$"3h;*HUxPVq)F/Fffq-%+AXESLABELSG6$Q"t6"Q!F`gr-%%VIEWG6$;FbfpFjep;$!2=tup.sRm"F^im$"2k9!>5\(Rm"F^im

omega:=5/2:plot([sol(t),env(t),-env(t)],t=0..20,color=[black,red,red]);

-%%PLOTG6'-%'CURVESG6$7\]l7$$""!F+F*7$$"39LLLL3VfV!#=$"3L6l'[%4&y%HF/7$$"3Kmm"z>5xI&F/$"3-9$HmYt]#QF/7$$"3\****\i&*)fD'F/$"3DU1X`In![%F/7$$"33m;zW#H,t'F/$"3@+dZ38(=o%F/7$$"3mKL3F*oU?(F/$"3-]z]MQ]yZF/7$$"3N+]P4'3%ywF/$"3;EiS.8:eZF/7$$"3%pmm;H[D:)F/$"33b]'faW5h%F/7$$"3'****\PpU&G5!#<$"3Mjq(f"=qyAF/7$$"3MLLLe0$=C"FS$!37i=<?O$**R#F/7$$"3[LLLLA`c9FS$!3guvK8?nxyF/7$$"3iLLL3RBr;FS$!36i'y5^(Qs6FS7$$"3)pTgF1Wzp"FS$!3/J0(fd1q>"FS7$$"37+v=<UlC<FS$!3;&*[Ph)G_@"FS7$$"3Z$e9;Pk8v"FS$!3-OMJMZwE7FS7$$"3#omTg_u!y<FS$!3U+3(Q^i8B"FS7$$"3=](o/o%y/=FS$!3u>U=y3")G7FS7$$"3`Le*[$[\J=FS$!3JN"**4.T*=7FS7$$"3)o"HK*)\?e=FS$!3OM[F5'G;?"FS7$$"3B++vV^"\)=FS$!3^7G"HK&zw6FS7$$"3WL$e9wb<*>FS$!3)z&RVtpO-5FS7$$"3imm;zjf)4#FS$!3!*4SaV'p'RrF/7$$"3aLLL38l(>#FS$!31il%QRicg$F/7$$"3-++]Piq'H#FS$"3`m&>!oJ$[<&!#>7$$"3[mmmm6w&R#FS$"3-;U!)*QJu#\F/7$$"3ULL$e4;[\#FS$"3DxGfw!RkF*F/7$$"37++]P<Q(f#FS$"3XYp"y@AEL"FS7$$"3#omm"zt%**p#FS$"3/G"4mvFIl"FS7$$"3=++++-B^FFS$"3M`Q$=!fqq<FS7$$"3`LL$3-8D!GFS$"37FT)QjQ_&=FS7$$"3@++DJW:GGFS$"374\d*4nT)=FS7$$"3)omm;%ez`GFS$"3J-5_Vl!Q!>FS7$$"36LL3_sVzGFS$"3so4idx"R">FS7$$"3!)****\i'y]!HFS$"3%zJHUx5V">FS7$$"3gLL$e>_6,$FS$"3g$>3K0d0"=FS7$$"3'pmm"HdA<JFS$"3'Goom/8#R:FS7$$"3K++]i#*HBKFS$"3]8Q)*zM,;6FS7$$"3oLL$ezs$HLFS$"3L=TtfZ_<dF/7$$"3#pm;HZRAQ$FS$"3ZS2O'HTVo#F/7$$"3=+++]h5NMFS$!3I5fbwlr#z%F[s7$$"3XLL3FG(z[$FS$!3c/b6&Hcaq$F/7$$"3qmm;/&R3a$FS$!3A^(=U#H[BpF/7$$"3'****\7=1Pf$FS$!32jF%elMh+"FS7$$"3ALLLeGdYOFS$!3Tb$>M8UZI"FS7$$"3YmmTN&R%*p$FS$!38Cas*Q87e"FS7$$"3=++]7iI_PFS$!3e0A_#fh*G=FS7$$"3'omTN'f1hQFS$!3C6<\muJBAFS7$$"3+MLe9d#)pRFS$!3,;e=&=x%GCFS7$$"3M]PM_c,(*RFS$!3uDnhGZsYCFS7$$"3omT5!f0U-%FS$!3)))*zSaD>^CFS7$$"3X$eky_&R^SFS$!3JX?***GP<W#FS7$$"3B+]ilaeySFS$!3g8+vqrH=CFS7$$"3!Q$e9T`'H8%FS$!3)p_>kwG'HBFS7$$"3Onmm;_M(=%FS$!3Zo=5#H]j=#FS7$$"3?MLek39$G%FS$!3XQK?7+U4=FS7$$"3/,+]7l$*yVFS$!3%e^I,]oVH"FS7$$"3YM$ekLMoU%FS$!3kj())zDi@&**F/7$$"3)ym;/;KZZ%FS$!3L7D8qY'*[nF/7$$"3I,]P%)*HE_%FS$!3o[*fMuh#*Q$F/7$$"3$QLL$3y_qXFS$"39"o"\6v>Io!#?7$$"3%pmTNT\Wi%FS$"3JM.(os3;+%F/7$$"3$4+](=5PyYFS$"3!))=DMsBD*yF/7$$"31M$eRi#HKZFS$"3&z&fLeO?l6FS7$$"3;nm;HU@'y%FS$"3N,hi$H@$>:FS7$$"3G+]PMe8S[FS$"37oSTfgKV=FS7$$"3QLLeRu0%*[FS$"3?!\A]e^&H@FS7$$"3Rn;zW!zz%\FS$"3,h8^A,8rBFS7$$"3]+++]1!>+&FS$"3rBbfw3;iDFS7$$"3[++]iO/c]FS$"3ydX$fY%H)p#FS7$$"3Y+++vm=5^FS$"3].8g'HX]x#FS7$$"3)3+]7=es8&FS$"3Q&GQ+\'R!z#FS7$$"3U++](oHV;&FS$"39\TYz,<!z#FS7$$"3'****\P>,9>&FS$"34$p>dG2Vx#FS7$$"3S++++FZ=_FS$"3-0.p'=RGu#FS7$$"3O+++D(enK&FS$"3qxF?T.qkCFS7$$"3J+++]Z/NaFS$"34S(*=^t_i>FS7$$"3_*****\d@s[&FS$"38\F.q`__;FS7$$"3h*******R)RRbFS$"3#)[qX5C`18FS7$$"3q*****\Av:f&FS$"3-!Gk_A<oJ*F/7$$"3!)******\?vVcFS$"3,f"Hn)ofd`F/7$$"3))*****\()Gfp&FS$"3_f&p*)p)Qq7F/7$$"3)********p0"[dFS$!3b"42KU.!fGF/7$$"33+++DDG+eFS$!3=&*HuS^bVpF/7$$"3;+++]$fC&eFS$!3jdDHi7p*3"FS7$$"3Sn"Hd!4%)**eFS$!3c%eM>=#GI9FS7$$"3xL$e9YAs%fFS$!3_W.R&Hqru"FS7$$"39+v=<Sg%*fFS$!3O/1%zU$zM?FS7$$"3Qnm"Hd&)>/'FS$!3wi,VRf4)G#FS7$$"35+]P%o[n8'FS$!3Oz+#=g(euEFS7$$"3qLL$ez6:B'FS$!3z(*>`S$G&zGFS7$$"3.<a8ACofiFS$!3#Q**30nmH!HFS7$$"3P+vV[I&yG'FS$!3([HUfE\)3HFS7$$"3/U&)eh$Q>I'FS$!3tNRv!R">0HFS7$$"3q$eRZnBgJ'FS$!3q"zmLRRr*GFS7$$"3PD1*y)*3,L'FS$!3%*RQm[eq%)GFS7$$"3/n;/,V>WjFS$!3xQp`t,"z'GFS7$$"3rLek`b`+kFS$!3s!['zA>tdFFS7$$"3P++D1o(oX'FS$!3I/+(4>h5e#FS7$$"30nT&)e!=K^'FS$!3s'pEU)**HUBFS7$$"3rL$e9Jf&plFS$!3^L&)R>FRZ?FS7$$"3Q+D1k0!fi'FS$!3&>(f:YQn.<FS7$$"3/nmm;=C#o'FS$!382B&\,!o>8FS7$$"3amm"zCq*HnFS$!3sX(\'*3H#*p*F/7$$"3!pmm"z')pxnFS$!3Wlp3=l(H/'F/7$$"3GnmT5rUDoFS$!3=.)HmBrGH#F/7$$"3knmmTb:toFS$"3u]m4b7w%["F/7$$"3,om"H(R)3#pFS$"3.F%>D&zIB_F/7$$"3]nm;/ChopFS$"3d?['**\zq&))F/7$$"3)pm;a$3M;qFS$"3u0p8o+DK7FS7$$"3Mnmmm#pS1(FS$"3yUn;2e#fb"FS7$$"3GMeky()e>rFS$"3s*[@Jvqi*=FS7$$"3K+]i!H3^<(FS$"3S&\8*)*fB!>#FS7$$"3QmTg-yiIsFS$"3#)4rQi45JCFS7$$"3JLLe9t9'G(FS$"3$y:%p0,Z8EFS7$$"3C+DcEomTtFS$"3&z"HsByRLFFS7$$"3=n;aQj=(R(FS$"30by<akZ)y#FS7$$"3l]7`%4Y\U(FS$"3SyV&)*Ry8z#FS7$$"36M3_]eq_uFS$"3Doi1"Q&)yx#FS7$$"3f</^1cY![(FS$"3e,C$4IW"[FFS7$$"3<++]i`A3vFS$"3PHKz4-S-FFS7$$"3Gm;a8P^1wFS$"3G6Hc7ot<CFS7$$"3GLLek?![q(FS$"3*zRb$Q9-i>FS7$$"3xmT5Si%Rv(FS$"3Js6[H_1"o"FS7$$"3G+]i:/4.yFS$"3H;NPW'=>P"FS7$$"3xLe9"fMA&yFS$"3ls*\:sC1/"FS7$$"3Rmmmm(y8!zFS$"3hI?id;#f$pF/7$$"3.Me9;xHbzFS$"3%p7E0WWj-$F/7$$"3y+]ilm@4!)FS$!32)H5"HCjM!*F[s7$$"3anT5:c8j!)FS$!3$o$[0T=&[w%F/7$$"3IMLekX0<")FS$!3"fAA?Zr<Z)F/7$$"3/,D19N(4<)FS$!3E$*p6n]F%>"FS7$$"3!ymTNY#*[A)FS$!3]v1rqXF5:FS7$$"3cM3-89")y#)FS$!3,@$>Bs"[)y"FS7$$"3K,+]i.tK$)FS$!3=$p&yb&fJ-#FS7$$"3u++vVvTN%)FS$!351FqDS*QL#FS7$$"3<+++DZ5Q&)FS$!3(RKo>Nn1X#FS7$$"3Q,+D1>zS')FS$!38]\n\S$*pBFS7$$"3!3++v3zMu)FS$!3iEaxTkc/@FS7$$"3EM3-Q20(z)FS$!33l9[d%o:!>FS7$$"3rn;a)QA1&))FS$!3-)R4,y(*4m"FS7$$"3=,D1RS>/*)FS$!3kvBgK,&*)Q"FS7$$"3jMLe*olx&*)FS$!3_Gd"z`H@4"FS7$$"34oT5StL6!*FS$!38l=e:/"ox(F/7$$"3b,]i!**3\1*FS$!3WE%R//c,`%F/7$$"3,Ne9T1[="*FS$!3O%e&)R9:jD"F/7$$"3Yomm"H_?<*FS$"3T-*Q"\Hjq>F/7$$"3@n;a)GV/F*FS$"3=?>9$Ry+a(F/7$$"3tnmT&GM)o$*FS$"3%)4akI#R8B"FS7$$"3Fo;H#GDsY*FS$"3E6#yiIKof"FS7$$"3,nm;zihl&*FS$"3)4S**f\c#G=FS7$$"33#eRZF[@f*FS$"3tXdDWM-m=FS7$$"3&*)\7.F!o='*FS$"3WZ9_'\<J*=FS7$$"3!eT&)eE7_k*FS$"395*pa&\`4>FS7$$"3lK$e9EW<n*FS$"3gH;<kRL:>FS7$$"3]\7.diF)p*FS$"3Y'\"*\UL1">FS7$$"3OmTg_#3[s*FS$"31/3Ci:h&*=FS7$$"3A$3x"[-M^(*FS$"3RmcpST]q=FS7$$"33++vVA(yx*FS$"3^\T8aBgN=FS7$$"3\n;/E-+%))*FS$"3x=Ds*\rcg"FS7$$"39LLL3#G,***FS$"3f4E7hw%[D"FS7$$"3@L3_Nl.55!#;$"3[3T]&)e@R!)F/7$$"3HL$3-Dg5-"Fh]n$"3sL_<z%pR8$F/7$$"3OLe*['R3K5Fh]n$!3f)3$**eu$*o;F/7$$"3WLLezw5V5Fh]n$!3)[ZL;zGc"fF/7$$"3tmmmJ+Ii5Fh]n$!31Q\,`q7'4"FS7$$"3.++v$Q#\"3"Fh]n$!3b>E/3(*yE7FS7$$"3nm;z\1A-6Fh]n$!3;RcM3<z&y*F/7$$"3]LL$e"*[H7"Fh]n$!3MlI6??"R'[F/7$$"3wmm"HCjV9"Fh]n$"3`+5V"3cXN%F[s7$$"3-+++qvxl6Fh]n$"3)3%)G&*o;z#RF/7$$"3=+DJ0],r6Fh]n$"3$)>!**Q9!ewVF/7$$"3;+]iSCDw6Fh]n$"3;m//KpVeYF/7$$"3:+v$f()*["="Fh]n$"3J+#oD^o!zZF/7$$"38++D6ts'="Fh]n$"3Z8n%RuB)[ZF/7$$"35+](==-s>"Fh]n$"3#yLH#[U#zH%F/7$$"31++]_qn27Fh]n$"3W![b.8%ziMF/7$$"33+]P/q%zA"Fh]n$"3GA]Z4VTz9F/7$$"36++Dcp@[7Fh]n$"3p]J(=ZA_S"F[s7$$"3,]ilPN%QD"Fh]n$"3%e7f(Rw?f:F`^l7$$"33+D1>,Zf7Fh]n$"3U3$zVE1Og"F`^l7$$"3@Dcw4MGi7Fh]n$"39Yq[cxW]jF`^l7$$"3;](o/q'4l7Fh]n$"3!3u8eDG$=9F[s7$$"36v=<"**4zE"Fh]n$"3b#4op"Rt+DF[s7$$"31+](=GB2F"Fh]n$"3'G*)3;AE"pQF[s7$$"3.+voWk(>G"Fh]n$"3Q2hNe]%>="F/7$$"3+++]2'HKH"Fh]n$"3Ls()Qt*e_C#F/7$$"3am;zu5M.8Fh]n$"3]J&3m7n3D$F/7$$"3ELL3UDX88Fh]n$"3wrhoH2,=TF/7$$"3rm"HdF3&=8Fh]n$"3UTks"p*fVWF/7$$"3)***\P4ScB8Fh]n$"3]]QCh$4'pYF/7$$"3EL3-V(>'G8Fh]n$"3*o?'y)=))zx%F/7$$"3_mmmwanL8Fh]n$"3I=4=I;b`ZF/7$$"3JLL$exn_N"Fh]n$"3[!)*=+"*4_&HF/7$$"35+++v+'oP"Fh]n$!3qHc(f%zq59F/7$$"3om;H2fU'R"Fh]n$!3')*Q"y2FqOkF/7$$"3CLLeR<*fT"Fh]n$!3/,(z=$oen5FS7$$"3i;/E&RR8U"Fh]n$!3#[Y-O%o"[9"FS7$$"3***\P40(oE9Fh]n$!3%[H^l$=.*>"FS7$$"3fTgxy3OH9Fh]n$!3D@Qd+8k;7FS7$$"3O$e9mqM?V"Fh]n$!3=nOypT_F7FS7$$"39DJXM&3ZV"Fh]n$!3=KPz.=VJ7FS7$$"3um;HiBQP9Fh]n$!3<Q*\^Jc"G7FS7$$"3\Lektw2[9Fh]n$!3[]s"*y[gS6FS7$$"3B+++&)Hxe9Fh]n$!3A,AXnC9L$*F/7$$"3ym"z%Rk$)o9Fh]n$!3fl')*>ag<P'F/7$$"3KL$eR*)**)y9Fh]n$!3o(3!f>rm5EF/7$$"30+vV[L'*)["Fh]n$"36%*=Ve:Z&o"F/7$$"3gmm"H!o-*\"Fh]n$"3a=d-q@x%='F/7$$"3*)****\7ga4:Fh]n$"3`S<#f[X+2"FS7$$"3PLL3A_1?:Fh]n$"3drsED(Q&f9FS7$$"3%omm;V%eI:Fh]n$"3[\&)=s5aY<FS7$$"39++DTO5T:Fh]n$"3[h`/kX*y*=FS7$$"3X$3-j'eCY:Fh]n$"3r*)*Hw7*G:>FS7$$"3vmTN"4)Q^:Fh]n$"3!Q)Q6`[E$*=FS7$$"31]iS;.`c:Fh]n$"3s6mYd**=J=FS7$$"3OL$e9as;c"Fh]n$"3R8/viFIH<FS7$$"3(**\i:*p&>d"Fh]n$"32NgN3PY69FS7$$"3emmmT9C#e"Fh]n$"3#H:wSYZ6f*F/7$$"34$eRZ([i(e"Fh]n$"3)e:5H@#G!z'F/7$$"3y*\7yI3If"Fh]n$"3V5A)*[!=bw$F/7$$"3Y;a)3u"R)f"Fh]n$"3pYZ!Qx&f=eF[s7$$"3;L$eR<vPg"Fh]n$!3g[;%3&=X!p#F/7$$"3%)\7.2'e"4;Fh]n$!3`%*fAk!Qv(fF/7$$"3`mT5S?a9;Fh]n$!3!)e*zbp-O?*F/7$$"3A$3xJZD*>;Fh]n$!37\)[ous#H7FS7$$"3"****\i!*3`i"Fh]n$!38*zX&e-2<:FS7$$"39L3-y'ycj"Fh]n$!3W7fXerI')>FS7$$"3rm;z\%[gk"Fh]n$!3$GoPRXGsI#FS7$$"3]$3xcLL7l"Fh]n$!3wUE8:MG,CFS7$$"3H+Dc@#=kl"Fh]n$!3+73P)>_qW#FS7$$"3^3_]k1,f;Fh]n$!3$*fk)oCL7X#FS7$$"3t;zW2Jgh;Fh]n$!3W!eB#e"eFW#FS7$$"3ID1R]b>k;Fh]n$!3Y\:i*\q:U#FS7$$"3_LLL$*zym;Fh]n$!3Aor,j?o(Q#FS7$$"3aL$3Fe#Rx;Fh]n$!3LL&eU0T'>@FS7$$"3bLL3sr*zo"Fh]n$!3t:w$=I<#f;FS7$$"3cL3xm%*H$p"Fh]n$!3;lfk!y>sO"FS7$$"3eL$e9w,')p"Fh]n$!3e'GaH+&eT5FS7$$"3eLe9cS!Rq"Fh]n$!3)H"yCh$40*oF/7$$"3fLL$3N1#4<Fh]n$!3a04:cEXqJF/7$$"3D]P%)RZY9<Fh]n$"3@[LEVRdFjF[s7$$"3#p;a)GJs><Fh]n$"3_CT%zm/#oWF/7$$"3e$eky^")\s"Fh]n$"3X.+q-RB`#)F/7$$"3C+](o!*R-t"Fh]n$"31A"G*4(R0>"FS7$$"3"pT&)eH)\N<Fh]n$"3_6!HH<IW`"FS7$$"3eLe*[oc2u"Fh]n$"3$[&)\n$HM\=FS7$$"3C]i!R2:gu"Fh]n$"3(Q'yIl#)=G@FS7$$"3!pm;HYt7v"Fh]n$"3rX&=T)>gkBFS7$$"39+vo*GP4w"Fh]n$"3Rk_vf">3n#FS7$$"3uL$ek6,1x"Fh]n$"3g!p0M<.5z#FS7$$"3)p;HK%\E!y"Fh]n$"3I/Ykx')o8FFS7$$"3A+++q(G**y"Fh]n$"3!y&Hi>_$=W#FS7$$"3gL3-)omaz"Fh]n$"3+EDP4/]/AFS7$$"3*pmTgg/5!=Fh]n$"3#[*yXo9,9>FS7$$"3Q+D1CDa1=Fh]n$"3(oC_H6qpd"FS7$$"3wLL3U/37=Fh]n$"3.![=+AU6?"FS7$$"3:nT5g$=w"=Fh]n$"3x.bHY(HF&zF/7$$"3a+]7yi:B=Fh]n$"3mdpdtuw)o$F/7$$"3$R$e9'>%pG=Fh]n$!3-Yle(z4$*z'F[s7$$"3'pmmT6KU$=Fh]n$!3)H)*4eO())\]F/7$$"3-+D1%H&=R=Fh]n$!3qjNzE*QX())F/7$$"3WL$eRZQT%=Fh]n$!3)y<T"GqSa7FS7$$"3&o;aQl"4\=Fh]n$!33%\aydH))f"FS7$$"3F++vL[/a=Fh]n$!3e7s>&>@T">FS7$$"35n;a$>^R'=Fh]n$!3mVZhyCxLCFS7$$"3dLLL`v&Q(=Fh]n$!38(4l4G)etFFS7$$"3)o"z>w'Q"z=Fh]n$!3fK;ZvjkrGFS7$$"3>+D1*z>W)=Fh]n$!3)[KhO_s(3HFS7$$"3n"z%\g.1()=Fh]n$!3'pPN!4!zT!HFS7$$"3]$3F>#4q*)=Fh]n$!3%H(*fG5`T)GFS7$$"3Mv$fL[TB*=Fh]n$!3hLq;zY!)[GFS7$$"3#om"zW?)\*=Fh]n$!3sN)o:mF$)z#FS7$$"3VL3_!HWb!>Fh]n$!3k]UA([z=X#FS7$$"30++DOl5;>Fh]n$!3_Yi$ej(f**=FS7$$"3;+voW7;@>Fh]n$!3T**RS-5$fd"FS7$$"3#***\7`f@E>Fh]n$!39U%)RriQA7FS7$$"3-+Dch1FJ>Fh]n$!343Z%G=x,Y)F/7$$"39+++q`KO>Fh]n$!3[<()zQ-?VXF/7$$"3C+vVy+QT>Fh]n$!3)4*))4e(\u]&F[s7$$"3O+](oyMk%>Fh]n$"3![=b>Q-"QMF/7$$"36+DJ&\*[^>Fh]n$"3Sv#RE`(fWtF/7$$"3A++v.Uac>Fh]n$"3I#3Xp6%>46FS7$$"3L]7Gyh(>'>Fh]n$"3C(f>B@#z&["FS7$$"33+D"G:3u'>Fh]n$"3XHHq__5F=FS7$$"3=]PMF,%G(>Fh]n$"3;)*[vNYaD@FS7$$"3H+](=5s#y>Fh]n$"3$f&RB*ybXP#FS7$$"3:+v$40O"*)>Fh]n$"3&\pPq#)3Tq#FS7$$"#?F+$"3ePp/A\"*)y#FS-%&COLORG6&%$RGBG$F+!""FjepFjep-F&6$7SF)7$F-$"3i`dA3CAkJF/7$FL$"3+pgsi=;))eF/7$FW$"3!\EN:p5r)))F/7$F[o$"3VE!)HJ")Q!="FS7$F]r$"3<VE()p2>d9FS7$Fbs$"3s4!HsIU!*p"FS7$Fju$"3kUf8pV)=$>FS7$F^w$"36]5Z*)QI^@FS7$Ffy$"3$yd*fOa&fM#FS7$F^\l$"34Q0f95#)=DFS7$F\^l$"3^/'*GLc[YEFS7$Fe`l$"3m%Q+Y3=6w#FS7$F]cl$"3Q#yMXySR%GFS7$Feel$"33:">WITA*GFS7$Fcgl$"3GfiRr"[)3HFS7$F_[m$"3QNJQ%*fi%*GFS7$Fg]m$"3nIhi=A$Q&GFS7$Fi`m$"3QD#)*GdCPx#FS7$Fgbm$"3LYL.O)pUn#FS7$F_em$"3Hx"*[Iq\NDFS7$Fcfm$"3%yO92$\%fP#FS7$F[im$"3]S*eul8G=#FS7$F_jm$"35G@u%\]L)>FS7$Fa]n$"3u`uKkjvY<FS7$Ff^n$"37j$))\[G-["FS7$F`_n$"3@15(fwlMB"FS7$Fj_n$"3KzhH+;xU&*F/7$Fd`n$"3%=%[oaZG^lF/7$Fbbn$"3Ww/%>eV=b$F/7$F\cn$"3/J%fCigK7'F[s7$Fden$!3$*p+jkccdEF/7$Fbgn$!3mdVk&R?#obF/7$F\hn$!3hj1&G*[W7')F/7$Ffhn$!3l@3p<"H&G6FS7$F^[o$!3ls3t&)[I39FS7$Fb\o$!3t4DLo6"pl"FS7$Ff]o$!3A<v8id"))*=FS7$Fd_o$!3a&*[t$[X]6#FS7$F\bo$!3%\1=')HMuJ#FS7$Fddo$!3r9PI44,([#FS7$Fbfo$!3pxG!o5"yKEFS7$Fjho$!3'p#y.BY8[FFS7$F^jo$!3c0PJ&[%QFGFS7$Ff\p$!3^Hn0(\Kd)GFS7$Fd^p$!3OIUx&Grz!HFS7$F\ap$!3bWdO=PF+HFS7$Fdcp$!3;?_Dq[iiGFS7$Fbep$!3/I"H**)yf*y#FS-Fgep6&Fiep$"#5F[fpFjepFjep-F&6$7SF)7$F-$!3i`dA3CAkJF/7$FL$!3+pgsi=;))eF/7$FW$!3!\EN:p5r)))F/7$F[o$!3VE!)HJ")Q!="FS7$F]r$!3<VE()p2>d9FS7$Fbs$!3s4!HsIU!*p"FS7$Fju$!3kUf8pV)=$>FS7$F^w$!36]5Z*)QI^@FS7$Ffy$!3$yd*fOa&fM#FS7$F^\l$!34Q0f95#)=DFS7$F\^l$!3^/'*GLc[YEFS7$Fe`l$!3m%Q+Y3=6w#FS7$F]cl$!3Q#yMXySR%GFS7$Feel$!33:">WITA*GFS7$Fcgl$!3GfiRr"[)3HFS7$F_[m$!3QNJQ%*fi%*GFS7$Fg]m$!3nIhi=A$Q&GFS7$Fi`m$!3QD#)*GdCPx#FS7$Fgbm$!3LYL.O)pUn#FS7$F_em$!3Hx"*[Iq\NDFS7$Fcfm$!3%yO92$\%fP#FS7$F[im$!3]S*eul8G=#FS7$F_jm$!35G@u%\]L)>FS7$Fa]n$!3u`uKkjvY<FS7$Ff^n$!37j$))\[G-["FS7$F`_n$!3@15(fwlMB"FS7$Fj_n$!3KzhH+;xU&*F/7$Fd`n$!3%=%[oaZG^lF/7$Fbbn$!3Ww/%>eV=b$F/7$F\cn$!3/J%fCigK7'F[s7$Fden$"3$*p+jkccdEF/7$Fbgn$"3mdVk&R?#obF/7$F\hn$"3hj1&G*[W7')F/7$Ffhn$"3l@3p<"H&G6FS7$F^[o$"3ls3t&)[I39FS7$Fb\o$"3t4DLo6"pl"FS7$Ff]o$"3A<v8id"))*=FS7$Fd_o$"3a&*[t$[X]6#FS7$F\bo$"3%\1=')HMuJ#FS7$Fddo$"3r9PI44,([#FS7$Fbfo$"3pxG!o5"yKEFS7$Fjho$"3'p#y.BY8[FFS7$F^jo$"3c0PJ&[%QFGFS7$Ff\p$"3^Hn0(\Kd)GFS7$Fd^p$"3OIUx&Grz!HFS7$F\ap$"3bWdO=PF+HFS7$Fdcp$"3;?_Dq[iiGFS7$Fbep$"3/I"H**)yf*y#FSF__q-%+AXESLABELSG6$Q"t6"Q!Fjhq-%%VIEWG6$;FjepFbep;$!1m!*o9K?DI!#:$"0.V,7-_-$!#9

omega:=1.75*sqrt(2):plot([sol(t),env(t),-env(t)],t=0..20,color=[black,red,red]);

-%%PLOTG6'-%'CURVESG6$7d]l7$$""!F+F*7$$"39LLLL3VfV!#=$"3b;0-B]SaHF/7$$"3Kmm"z>5xI&F/$"3s9:5-,_QQF/7$$"3\****\i&*)fD'F/$"3cwJ#z3MX]%F/7$$"33m;zW#H,t'F/$"3)=QV3&*GBr%F/7$$"3mKL3F*oU?(F/$"3+d7#[(3X;[F/7$$"3N+]P4'3%ywF/$"3%39`qN/W![F/7$$"3%pmm;H[D:)F/$"3z$*o$z/+jm%F/7$$"3'****\PpU&G5!#<$"3b'3D&z*=wP#F/7$$"3MLLLe0$=C"FS$!3kBsxzwvsAF/7$$"3SLL$eR"=\8FS$!3)4bVy'>@f]F/7$$"3[LLLLA`c9FS$!345-&zGH4x(F/7$$"3bLL$32$)Qc"FS$!3Yvs!Gy/!45FS7$$"3iLLL3RBr;FS$!3v=x@#Qb5<"FS7$$"3)pTgF1Wzp"FS$!3!z6)QcMO(>"FS7$$"37+v=<UlC<FS$!3e0Lk`)zt@"FS7$$"3Z$e9;Pk8v"FS$!3id))HE(33B"FS7$$"3#omTg_u!y<FS$!3)fU%)4:"RP7FS7$$"3=](o/o%y/=FS$!3`@6&[a2pB"FS7$$"3`Le*[$[\J=FS$!3g<,R\)z"H7FS7$$"3)o"HK*)\?e=FS$!3QxSYkM297FS7$$"3B++vV^"\)=FS$!3O"4$o;*)\">"FS7$$"3WL$e9wb<*>FS$!3.vGm_&yj-"FS7$$"3imm;zjf)4#FS$!3BA*pP=e-Z(F/7$$"3aLLL38l(>#FS$!3'f5kP%Ry3SF/7$$"3-++]Piq'H#FS$"3l*R=&zHYfh!#?7$$"3[mmmm6w&R#FS$"3Y")Hc=vpYWF/7$$"3ULL$e4;[\#FS$"3th`iOPh0))F/7$$"37++]P<Q(f#FS$"3c%*yT"4C2H"FS7$$"3#omm"zt%**p#FS$"3W'HO$*)Gt?;FS7$$"3`LL$3-8D!GFS$"31%GXFzln$=FS7$$"3!)****\i'y]!HFS$"3'Rd&*GjaK">FS7$$"3gLL$e>_6,$FS$"3`IJQ6T=I=FS7$$"3'pmm"HdA<JFS$"3A-,561p!e"FS7$$"3K++]i#*HBKFS$"3L:ATNSjy6FS7$$"3oLL$ezs$HLFS$"3!Q^jL"erFlF/7$$"3#pm;HZRAQ$FS$"3hSf*z[\'pNF/7$$"3=+++]h5NMFS$"3#*Rxa?k_pY!#>7$$"3XLL3FG(z[$FS$!3Ebb2B*fYr#F/7$$"3qmm;/&R3a$FS$!3+I^JxQM1fF/7$$"3'****\7=1Pf$FS$!3e*>TW4lw.*F/7$$"3ALLLeGdYOFS$!3y"oXX@?Q?"FS7$$"3YmmTN&R%*p$FS$!3g6Er:u"R["FS7$$"3=++]7iI_PFS$!3;Q!Gkb0vt"FS7$$"3'omTN'f1hQFS$!3cN'=(GWs]@FS7$$"3+MLe9d#)pRFS$!3]m%*y*3>KQ#FS7$$"3M]PM_c,(*RFS$!3nN*\w/Z%4CFS7$$"3omT5!f0U-%FS$!3wKN1Q**GACFS7$$"3X$eky_&R^SFS$!3/!)3p!*oc@CFS7$$"3B+]ilaeySFS$!3Q*[k4uvrS#FS7$$"3!Q$e9T`'H8%FS$!3;j$)Q00QPBFS7$$"3Onmm;_M(=%FS$!3rt@[jJp8AFS7$$"3?MLek39$G%FS$!3=>a6%ok<(=FS7$$"3/,+]7l$*yVFS$!3qU3PV(z-R"FS7$$"3YM$ekLMoU%FS$!3>ch=v6g16FS7$$"3)ym;/;KZZ%FS$!3ba=c!QjZ+)F/7$$"3I,]P%)*HE_%FS$!3LXVd)G88x%F/7$$"3$QLL$3y_qXFS$!3_F$)yYId@9F/7$$"3%pmTNT\Wi%FS$"3<5ju"e5bT#F/7$$"3$4+](=5PyYFS$"3_gMe)yd)RiF/7$$"31M$eRi#HKZFS$"3K6gEZ70l**F/7$$"3;nm;HU@'y%FS$"3tnA&p&Gh]8FS7$$"3G+]PMe8S[FS$"3m47U#>e"y;FS7$$"3QLLeRu0%*[FS$"3Hkq>^"H:(>FS7$$"3Rn;zW!zz%\FS$"3T,ZU(eMQA#FS7$$"3]+++]1!>+&FS$"3\0#)3[/2HCFS7$$"3[++]iO/c]FS$"3'[3'QZAy#e#FS7$$"3Y+++vm=5^FS$"3$3?imon,o#FS7$$"3)3+]7=es8&FS$"3uJz5N$yoq#FS7$$"3U++](oHV;&FS$"3!y,h^kT'=FFS7$$"3'****\P>,9>&FS$"3y7F_<ZM:FFS7$$"3S++++FZ=_FS$"3QP$)e#4hpp#FS7$$"3O+++D(enK&FS$"3F%GkPDj]Z#FS7$$"3J+++]Z/NaFS$"3Bm!*eM]&>.#FS7$$"3_*****\d@s[&FS$"33^X([]q*\<FS7$$"3h*******R)RRbFS$"3[+:"*GH$4V"FS7$$"3q*****\Av:f&FS$"3,_(y"G$493"FS7$$"3!)******\?vVcFS$"3/:E!>#=P'3(F/7$$"3))*****\()Gfp&FS$"3jc\bhDp.KF/7$$"3)********p0"[dFS$!3q-2hV&G$HvFbw7$$"33+++DDG+eFS$!3fX6Pjxv+ZF/7$$"3;+++]$fC&eFS$!3)\lCxm!4d&)F/7$$"3Sn"Hd!4%)**eFS$!3%QIS+py6>"FS7$$"3xL$e9YAs%fFS$!3KFZ">%*Hm]"FS7$$"39+v=<Sg%*fFS$!3woO5y!4mz"FS7$$"3Qnm"Hd&)>/'FS$!3Wd<!Gg3h0#FS7$$"35+]P%o[n8'FS$!3jW!>Q.(RmCFS7$$"3qLL$ez6:B'FS$!3n"p,eq/&4FFS7$$"3.<a8ACofiFS$!3(HtdQ`4ou#FS7$$"3P+vV[I&yG'FS$!3,?_Bg]gnFFS7$$"3q$eRZnBgJ'FS$!3\Eu\wEyrFFS7$$"3/n;/,V>WjFS$!3I8gy\rLfFFS7$$"3rLek`b`+kFS$!38msde92&o#FS7$$"3P++D1o(oX'FS$!3C-S3(*R"oa#FS7$$"30nT&)e!=K^'FS$!3m%RvjF^"[BFS7$$"3rL$e9Jf&plFS$!3'4h>)f\:%4#FS7$$"3Q+D1k0!fi'FS$!3=JCSw([7z"FS7$$"3/nmm;=C#o'FS$!3/-nHm7/Z9FS7$$"3amm"zCq*HnFS$!37bAuH')\H6FS7$$"3!pmm"z')pxnFS$!3SKC8ZRRTzF/7$$"3GnmT5rUDoFS$!3!)Ht;.!3#pWF/7$$"3knmmTb:toFS$!35kKp!*p:)R*Fbw7$$"3,om"H(R)3#pFS$"3unJ1CCq%e#F/7$$"3]nm;/ChopFS$"3o?GA(e,F/'F/7$$"3)pm;a$3M;qFS$"3o_\nT#)3u$*F/7$$"3Mnmmm#pS1(FS$"3mg@J9,9_7FS7$$"3GMeky()e>rFS$"3[%GoP;uze"FS7$$"3K+]i!H3^<(FS$"3JV0)p$z'R)=FS7$$"3QmTg-yiIsFS$"3%\7F_[vM8#FS7$$"3JLLe9t9'G(FS$"3m/RXV3.JBFS7$$"3C+DcEomTtFS$"33tOju@ZsCFS7$$"3=n;aQj=(R(FS$"3Gk,"3MK]b#FS7$$"3l]7`%4Y\U(FS$"3T">QZ*GwtDFS7$$"36M3_]eq_uFS$"3-X15eQRxDFS7$$"3f</^1cY![(FS$"3GlUVV+*fc#FS7$$"3<++]i`A3vFS$"3Y>QTArqRDFS7$$"3Gm;a8P^1wFS$"3E#ym\2(\JBFS7$$"3GLLek?![q(FS$"3Y&QgD$3?g>FS7$$"3xmT5Si%Rv(FS$"3uUS))oXtA<FS7$$"3G+]i:/4.yFS$"33"eF3XopX"FS7$$"3xLe9"fMA&yFS$"3*zimp_6#o6FS7$$"3Rmmmm(y8!zFS$"3%fsZG0V9i)F/7$$"3.Me9;xHbzFS$"3La^wD!=[8&F/7$$"3y+]ilm@4!)FS$"3Ibu$GLq:f"F/7$$"3anT5:c8j!)FS$!3>h)**[-Zz#>F/7$$"3IMLekX0<")FS$!3Mty!)y8;X`F/7$$"3/,D19N(4<)FS$!34#)>lE]4&e)F/7$$"3!ymTNY#*[A)FS$!3]#Q$)y&p!y:"FS7$$"3cM3-89")y#)FS$!3'y$)>@+EhU"FS7$$"3K,+]i.tK$)FS$!3dg![ME1!e;FS7$$"3u++vVvTN%)FS$!3sK=%px*Q$)>FS7$$"3<+++DZ5Q&)FS$!3cPfHPmOS@FS7$$"3O,DJ?lxj&)FS$!3IPNDT"pA:#FS7$$"3x+]i:$[%*e)FS$!3`'yY(QID`@FS7$$"3=+v$46?^h)FS$!3OUg2'QGM9#FS7$$"3Q,+D1>zS')FS$!3!*4u$3UhH7#FS7$$"3=+](o\N@p)FS$!3Rcnk!fP50#FS7$$"3!3++v3zMu)FS$!3K`gO&)Q()R>FS7$$"3rn;a)QA1&))FS$!3!4@s9xcif"FS7$$"3jMLe*olx&*)FS$!3#p]lR8?U8"FS7$$"34oT5StL6!*FS$!3lIzvn?!>t)F/7$$"3b,]i!**3\1*FS$!31JU.?=X0gF/7$$"3,Ne9T1[="*FS$!3]I]gF=aFKF/7$$"3Yomm"H_?<*FS$!3'*ok6p/wBYFbw7$$"3@n;a)GV/F*FS$"3Jb3LX@>yVF/7$$"3tnmT&GM)o$*FS$"3QtY>gk==')F/7$$"3Fo;H#GDsY*FS$"3UGzdcPD(>"FS7$$"3,nm;zihl&*FS$"3CXz)eK0TU"FS7$$"3&*)\7.F!o='*FS$"3w*=?(32M(\"FS7$$"3lK$e9EW<n*FS$"3(H+iWr6a`"FS7$$"3]\7.diF)p*FS$"3m(yjj7m8a"FS7$$"3OmTg_#3[s*FS$"3jf`))*ye(Q:FS7$$"3A$3x"[-M^(*FS$"378=-U1xF:FS7$$"33++vVA(yx*FS$"3!3%)eV")H'3:FS7$$"3\n;/E-+%))*FS$"3=FxjGzic8FS7$$"39LLL3#G,***FS$"3![e(*Hn[I5"FS7$$"3@L3_Nl.55!#;$"3J%zg#zy(*ewF/7$$"3HL$3-Dg5-"Fd\n$"3.f**fckpJRF/7$$"3OLe*['R3K5Fd\n$"3OPo2\\*[_#Fbw7$$"3WLLezw5V5Fd\n$!3aIgol?3:IF/7$$"3tmmmJ+Ii5Fd\n$!3!eW#p6"pd#pF/7$$"3.++v$Q#\"3"Fd\n$!30Dbop'))*Q!)F/7$$"3nm;z\1A-6Fd\n$!3gU"HkKXjX'F/7$$"3]LL$e"*[H7"Fd\n$!3Mx8`k,STLF/7$$"3wmm"HCjV9"Fd\n$!34k5"p'RS-MFbw7$$"3-+++qvxl6Fd\n$"3v%)=zI()Qo5F/7$$"3=+DJ0],r6Fd\n$"3u'3'o96M66F/7$$"3;+]iSCDw6Fd\n$"3!))[DQ=kP/"F/7$$"3:+v$f()*["="Fd\n$"3*\!)R^)z)>x)Fbw7$$"38++D6ts'="Fd\n$"3GP`mX&R&oiFbw7$$"35+](==-s>"Fd\n$!3iBN&\Mld%\Fes7$$"31++]_qn27Fd\n$!3,9izakZO")Fbw7$$"3;+vVG?"y@"Fd\n$!3OpD?Fz?h9F/7$$"33+]P/q%zA"Fd\n$!33!*QRY^7d=F/7$$"39]PM#\9IB"Fd\n$!3e!frw;3(=>F/7$$"3,+DJ!)>3Q7Fd\n$!3-=gsq%=C(=F/7$$"31]7Go%\JC"Fd\n$!3)>(f_P%)y4<F/7$$"36++Dcp@[7Fd\n$!3e`B&e5$=E9F/7$$"31+](=GB2F"Fd\n$"3MDK%4o)R;7F/7$$"3+++]2'HKH"Fd\n$"3Yx)=&RcVB_F/7$$"3am;zu5M.8Fd\n$"3K'ftm$\!e$pF/7$$"3ELL3UDX88Fd\n$"3IEa2ovE%G)F/7$$"3rm"HdF3&=8Fd\n$"3^gT$oZ_jv)F/7$$"3)***\P4ScB8Fd\n$"3T$G1g">%G1*F/7$$"3EL3-V(>'G8Fd\n$"30oz@Uw\%=*F/7$$"3_mmmwanL8Fd\n$"3w^N"**phf5*F/7$$"3$)***\iirWM"Fd\n$"3=]MZRg.C#)F/7$$"3JLL$exn_N"Fd\n$"3TzcSmfvcjF/7$$"3zmmTDR1m8Fd\n$"3NKE*)*)))e'e$F/7$$"35+++v+'oP"Fd\n$"3"\TGFYb02"Fbw7$$"3HLe9"*Hk'Q"Fd\n$!3kF:$\>=lT$F/7$$"3om;H2fU'R"Fd\n$!3=p`'[&)4`,(F/7$$"3/+vVB)3iS"Fd\n$!34;y'oJQ#R5FS7$$"3CLLeR<*fT"Fd\n$!3"Hwhx)*pZK"FS7$$"3***\P40(oE9Fd\n$!3!G#*R6j"pW:FS7$$"3um;HiBQP9Fd\n$!39-)[$yy!*R;FS7$$"3M3-8!>c+W"Fd\n$!3iG&3L+R<k"FS7$$"36](oz,IFW"Fd\n$!3Cwp&*RONM;FS7$$"3*=H2e%QSX9Fd\n$!3%RUN\`Hwh"FS7$$"3\Lektw2[9Fd\n$!3i3,"HO*\"f"FS7$$"3'o"HKH`U`9Fd\n$!3=Y/j0I.6:FS7$$"3B+++&)Hxe9Fd\n$!3%**3/CX^NR"FS7$$"3ym"z%Rk$)o9Fd\n$!3Q#G%*31@"y5FS7$$"3KL$eR*)**)y9Fd\n$!3\z3iO(GIc'F/7$$"3p;z>@;$R["Fd\n$!3bs4/=ubTTF/7$$"30+vV[L'*)["Fd\n$!3?*3V>HL"p:F/7$$"3S$3xc2&*R\"Fd\n$"3&4V-.&zm06F/7$$"3gmm"H!o-*\"Fd\n$"3cpt/x$44$QF/7$$"3LL$3xS'G/:Fd\n$"3V'ze,J,Yn'F/7$$"3*)****\7ga4:Fd\n$"3'4n2W;v2X*F/7$$"3jm;H<c![^"Fd\n$"3S6Gw'\5'47FS7$$"3PLL3A_1?:Fd\n$"3?%4\[lv[X"FS7$$"3%omm;V%eI:Fd\n$"3tmL\\F\k=FS7$$"39++DTO5T:Fd\n$"3s5%oBI)*G8#FS7$$"3X$3-j'eCY:Fd\n$"3X'>*>Z%[J?#FS7$$"3vmTN"4)Q^:Fd\n$"3I)G"G!*\&*HAFS7$$"3T3-)Q?fRb"Fd\n$"3_r9]$G%eEAFS7$$"31]iS;.`c:Fd\n$"3*3/%Gj!*)=@#FS7$$"3r"HK*G95f:Fd\n$"3%=C*enr$e=#FS7$$"3OL$e9as;c"Fd\n$"3p?LC'pc%[@FS7$$"3(**\i:*p&>d"Fd\n$"3/*4sHEI$))=FS7$$"3emmmT9C#e"Fd\n$"3`C$Qi?3[Y"FS7$$"34$eRZ([i(e"Fd\n$"3Y\X5u')R(="FS7$$"3y*\7yI3If"Fd\n$"3%\i2`<M$)y)F/7$$"3Y;a)3u"R)f"Fd\n$"3#ff?'=g6caF/7$$"3;L$eR<vPg"Fd\n$"34&o=1Jd!\>F/7$$"3%)\7.2'e"4;Fd\n$!3i'\2kQ%)fl"F/7$$"3`mT5S?a9;Fd\n$!3Id#e#\Pwy_F/7$$"3A$3xJZD*>;Fd\n$!3!zr)ota\P))F/7$$"3"****\i!*3`i"Fd\n$!3#Gz#zCh2D7FS7$$"3q;a8#z$\I;Fd\n$!3q_()\R/nK:FS7$$"39L3-y'ycj"Fd\n$!35-nUgDs7=FS7$$"3#*\i!Rcj3k"Fd\n$!3')*3C_dN!f?FS7$$"3rm;z\%[gk"Fd\n$!3zl!y^HigE#FS7$$"3H+Dc@#=kl"Fd\n$!3S!ymK$\1WDFS7$$"3_LLL$*zym;Fd\n$!34`4+Izw>EFS7$$"3aL$3Fe#Rx;Fd\n$!3u/N>ymMxCFS7$$"3bLL3sr*zo"Fd\n$!3["prU%\)47#FS7$$"3cL3xm%*H$p"Fd\n$!3G?K_POWq=FS7$$"3eL$e9w,')p"Fd\n$!3Y$GN+y!4y:FS7$$"3eLe9cS!Rq"Fd\n$!3#\u!epz(*\7FS7$$"3fLL$3N1#4<Fd\n$!3!oTGkk%*)H*)F/7$$"3D]P%)RZY9<Fd\n$!3K./$))p1*y^F/7$$"3#p;a)GJs><Fd\n$!3!RpkMaurH"F/7$$"3e$eky^")\s"Fd\n$"3!*o=O(=&=LEF/7$$"3C+](o!*R-t"Fd\n$"3Ek"*Qb1dGlF/7$$"3"pT&)eH)\N<Fd\n$"3'pr?NTt0."FS7$$"3eLe*[oc2u"Fd\n$"3Tfv#R7i$)Q"FS7$$"3C]i!R2:gu"Fd\n$"3#fhJK#o^=<FS7$$"3!pm;HYt7v"Fd\n$"3CTfmW;!R,#FS7$$"39+vo*GP4w"Fd\n$"3e:HX%fF`W#FS7$$"3uL$ek6,1x"Fd\n$"3,2GP^Ak1FFS7$$"3'>/^J2<Ix"Fd\n$"3#zMh$=u#Gu#FS7$$"3=]P%)HIVv<Fd\n$"3#*Ql%R=Jpw#FS7$$"3Sek`')*[yx"Fd\n$"38P+5"3P)yFFS7$$"3)p;HK%\E!y"Fd\n$"3Jx[XhV[yFFS7$$"3x$e9m&o4&y"Fd\n$"3GU"pJGS5u#FS7$$"3A+++q(G**y"Fd\n$"3Pz9v/EBbEFS7$$"3gL3-)omaz"Fd\n$"3g5$o.t0%*\#FS7$$"3*pmTgg/5!=Fd\n$"3!Q:$oPet&G#FS7$$"3Q+D1CDa1=Fd\n$"3#))o+)=HF>?FS7$$"3wLL3U/37=Fd\n$"3'Qm8"*QIjq"FS7$$"3:nT5g$=w"=Fd\n$"3jN?hT/La8FS7$$"3a+]7yi:B=Fd\n$"3N/Qs!y?ir*F/7$$"3$R$e9'>%pG=Fd\n$"3C"e*RwSwscF/7$$"3'pmmT6KU$=Fd\n$"35#eP+xV'3:F/7$$"3-+D1%H&=R=Fd\n$!32`c\tejPAF/7$$"3WL$eRZQT%=Fd\n$!3c>EL6z6JfF/7$$"3&o;aQl"4\=Fd\n$!3`yUG%QzB]*F/7$$"3F++vL[/a=Fd\n$!3)pR#[[jX)G"FS7$$"3oLek8!)**e=Fd\n$!3!Rs;w^n9g"FS7$$"35n;a$>^R'=Fd\n$!3gFwGG'zM)=FS7$$"3^+vVtV!*o=Fd\n$!3ghBO(e>$H@FS7$$"3dLLL`v&Q(=Fd\n$!3OUfm&RJXL#FS7$$"3)o"z>w'Q"z=Fd\n$!3"e\+&p)yW]#FS7$$"3>+D1*z>W)=Fd\n$!3_+=jdcv?EFS7$$"3n"z%\g.1()=Fd\n$!3!)G#o6gZ!eEFS7$$"3]$3F>#4q*)=Fd\n$!32&3E!\3@"o#FS7$$"3Mv$fL[TB*=Fd\n$!3!\))\"\"p,p#FS7$$"3#om"zW?)\*=Fd\n$!3i9Ce$>C\o#FS7$$"3VL3_!HWb!>Fd\n$!3\GoiIqkCDFS7$$"30++DOl5;>Fd\n$!3*zP[L$z'p:#FS7$$"3;+voW7;@>Fd\n$!32e&HfD$=<>FS7$$"3#***\7`f@E>Fd\n$!3k*3[S!*)oU;FS7$$"3-+Dch1FJ>Fd\n$!3Z;v>%4">R8FS7$$"39+++q`KO>Fd\n$!31k8vhd#H,"FS7$$"3C+vVy+QT>Fd\n$!3!*=4eN%o_q'F/7$$"3O+](oyMk%>Fd\n$!31G#zPst))=$F/7$$"36+DJ&\*[^>Fd\n$"3Q99>YPO)\$Fbw7$$"3A++v.Uac>Fd\n$"3yHN!Qka5%QF/7$$"3L]7Gyh(>'>Fd\n$"38Z"y)))=;iuF/7$$"33+D"G:3u'>Fd\n$"3z&y!yBR$p3"FS7$$"3=]PMF,%G(>Fd\n$"3A9Kosi!))R"FS7$$"3H+](=5s#y>Fd\n$"3?&G)elf9v;FS7$$"3:+v$40O"*)>Fd\n$"3w"H<Cps"*4#FS7$$"#?F+$"3+B9K:h&eK#FS-%&COLORG6&%$RGBG$F+!""FbhpFbhp-F&6$7SF)7$F-$"3-_7`(R&4yJF/7$FL$"3g`'4Ula4"fF/7$FW$"3m!>RL?KI"*)F/7$Feo$"3jXcmL?@#="FS7$Fgr$"3bUopG)QoX"FS7$F\t$"3U'\]r#\:&p"FS7$F`u$"3(f`'3A9dA>FS7$Fdv$"3uTz^\IHM@FS7$F]y$"3)4'*=fO/!>BFS7$Fe[l$"30*)y'=Fx"zCFS7$Fc]l$"3Opdn%f_Nf#FS7$F[`l$"3C[.!3;y3p#FS7$Fcbl$"3o%QlZf1Rv#FS7$F[el$"3#)\km(o&)4y#FS7$Fifl$"3T_QNLcmwFFS7$F[jl$"3+fK;FHyNFFS7$Fc\m$"3"zqVb&*o6n#FS7$Fe_m$"3I"))=I)fJiDFS7$Fcam$"3%ppX=XioV#FS7$F[dm$"3E"e'4#RI%pAFS7$Fcfm$"3ikJ=y0$H3#FS7$Fahm$"3q>;WpGdi=FS7$Feim$"3&)e1>s=RR;FS7$F]\n$"3m88cO!G"z8FS7$Fb]n$"3?y>l*e524"FS7$F\^n$"3.fOm$H=hF)F/7$Ff^n$"3=T`+xf0T`F/7$F`_n$"3%34$RUj'GC#F/7$F^an$!3l!\>oG5!e")Fbw7$F\cn$!3<jWK24@mPF/7$Ffcn$!3['fIk9n2*pF/7$Fden$!3pfa'4d`i!)*F/7$Fhfn$!3v)R.%4c'*o7FS7$F\hn$!3=nR.uiE;:FS7$Fdjn$!3<N=T_NCo<FS7$Fb\o$!30Q$[zwO])>FS7$F`^o$!3#>FL?tIz=#FS7$Fh`o$!3)zYC]j@0O#FS7$F`co$!3W+h(Hs*p6DFS7$F^eo$!3sp&3k["*pi#FS7$F\go$!3w-bkq=p7FFS7$Fdio$!3mdUaDl[kFFS7$F\\p$!3Ku!y"RWQ#y#FS7$Fd^p$!31k<Y"3"onFFS7$F\ap$!3p7e#oT@Gs#FS7$Fdcp$!3vNw)yDtDk#FS7$F\fp$!3lf'[%REKNDFS7$Fjgp$!3X4uE"[x#)Q#FS-F_hp6&Fahp$"#5FchpFbhpFbhp-F&6$7SF)7$F-$!3-_7`(R&4yJF/7$FL$!3g`'4Ula4"fF/7$FW$!3m!>RL?KI"*)F/7$Feo$!3jXcmL?@#="FS7$Fgr$!3bUopG)QoX"FS7$F\t$!3U'\]r#\:&p"FS7$F`u$!3(f`'3A9dA>FS7$Fdv$!3uTz^\IHM@FS7$F]y$!3)4'*=fO/!>BFS7$Fe[l$!30*)y'=Fx"zCFS7$Fc]l$!3Opdn%f_Nf#FS7$F[`l$!3C[.!3;y3p#FS7$Fcbl$!3o%QlZf1Rv#FS7$F[el$!3#)\km(o&)4y#FS7$Fifl$!3T_QNLcmwFFS7$F[jl$!3+fK;FHyNFFS7$Fc\m$!3"zqVb&*o6n#FS7$Fe_m$!3I"))=I)fJiDFS7$Fcam$!3%ppX=XioV#FS7$F[dm$!3E"e'4#RI%pAFS7$Fcfm$!3ikJ=y0$H3#FS7$Fahm$!3q>;WpGdi=FS7$Feim$!3&)e1>s=RR;FS7$F]\n$!3m88cO!G"z8FS7$Fb]n$!3?y>l*e524"FS7$F\^n$!3.fOm$H=hF)F/7$Ff^n$!3=T`+xf0T`F/7$F`_n$!3%34$RUj'GC#F/7$F^an$"3l!\>oG5!e")Fbw7$F\cn$"3<jWK24@mPF/7$Ffcn$"3['fIk9n2*pF/7$Fden$"3pfa'4d`i!)*F/7$Fhfn$"3v)R.%4c'*o7FS7$F\hn$"3=nR.uiE;:FS7$Fdjn$"3<N=T_NCo<FS7$Fb\o$"30Q$[zwO])>FS7$F`^o$"3#>FL?tIz=#FS7$Fh`o$"3)zYC]j@0O#FS7$F`co$"3W+h(Hs*p6DFS7$F^eo$"3sp&3k["*pi#FS7$F\go$"3w-bkq=p7FFS7$Fdio$"3mdUaDl[kFFS7$F\\p$"3Ku!y"RWQ#y#FS7$Fd^p$"31k<Y"3"onFFS7$F\ap$"3p7e#oT@Gs#FS7$Fdcp$"3vNw)yDtDk#FS7$F\fp$"3lf'[%REKNDFS7$Fjgp$"3X4uE"[x#)Q#FSFgaq-%+AXESLABELSG6$Q"t6"Q!Fb[r-%%VIEWG6$;FbhpFjgp;$!1(>Xn")zO*G!#:$"1(>Xn")zO*GF[\r

omega:=29/10:plot([sol(t),env(t),-env(t)],t=0..50,color=[black,red,red]);

-%%PLOTG6'-%'CURVESG6$7ifm7$$""!F+F*7$$"3\LL$3FWYs#!#=$"3;#eWaN8*H8F/7$$"3)pmm;a)G\aF/$"3YWm'=Z#["p$F/7$$"3!HL$3x1h6oF/$"3m!*\<j`1!=%F/7$$"3"*****\7G$R<)F/$"3-g*)fx\p&p$F/7$$"3%pm;z%\DO&*F/$"3ma9gUqU%3#F/7$$"3RLLL3x&)*3"!#<$!35WPVS'GBU&!#>7$$"3em"z%\v#pK"FI$!3B(\<(f%[iF'F/7$$"3)***\i!R(*Rc"FI$!3[LsYNB6a5FI7$$"3n;z>6B`#o"FI$!3$=)zR,'HO5"FI7$$"3RL3xJs1,=FI$!3`4HX"p,f+"FI7$$"34]PM_@g>>FI$!3!*4erE!HRb(F/7$$"3zmm"H2P"Q?FI$!3#>+R6OQ$)o$F/7$$"3YLek.pu/BFI$"31eh+R08!p(F/7$$"36+]PMnNrDFI$"3@=,$>:8in"FI7$$"37#Hd?>4!QEFI$"3@dj\Gxpy<FI7$$"3n$eR(\;m/FFI$"3j#)\!p*R(Q"=FI7$$"3Bv=U2TJrFFI$"34+1azA&px"FI7$$"3ymT5ll'z$GFI$"3]WPk;"4gm"FI7$$"3*)\(o/[r7(HFI$"3<[!\W[(yH7FI7$$"3XLL$eRwX5$FI$"3>B-.x6R;bF/7$$"3tLLe*[`HP$FI$!35p'o$\(y:9"FI7$$"3fLLL$eI8k$FI$!3<N&RiiFlP#FI7$$"3yL3xc[U3PFI$!3+tZuUY#f\#FI7$$"3'RL3-8>bx$FI$!32dl!)RH")=DFI7$$"39Mek.MhUQFI$!3e#*QNa*G3W#FI7$$"3*QL$3xwq4RFI$!3+9b)Ht];E#FI7$$"3"QLeRA'*Q/%FI$!3**4**QrHK>;FI7$$"3<ML$3x%3yTFI$!3S")HCC$p@r'F/7$$"3GnT5:j=XWFI$"3eIJBv_Wa:FI7$$"3Q+]PfyG7ZFI$"3s61q4jhxIFI7$$"3(\&)3Cbvcu%FI$"3#G'z6n2DdJFI7$$"3m3FWXK1zZFI$"3(GZ%\ra'o?$FI7$$"3OilZQ4X7[FI$"3oe7#y$\bDKFI7$$"3$pT5:jQe%[FI$"3I:v#QC7F@$FI7$$"3@D"yv,9E"\FI$"3'fhIFc_:4$FI7$$"3\Lek.%*Qz\FI$"3M*ec#[k![%GFI7$$"3/]7yv,%H6&FI$"39WBWrld0?FI7$$"3fmm"z%4\Y_FI$"3NqX"R#oCW!)F/7$$"3aKL$3FGT\&FI$!3*4E"[)p%[i<FI7$$"3S***\Pfl<u&FI$!3*>>-rkr*=OFI7$$"36m"zW#\n.eFI$!3k^I_^&H9$QFI7$$"3"GL3_D%eleFI$!3d_kq1wq=RFI7$$"3;;Hd?*Ql*eFI$!3D`7-Tx\8RFI7$$"3`*\Pfe$\FfFI$!3b%))*R**QCvQFI7$$"3)G3-8D[%efFI$!36$Q9@MNR!QFI7$$"3Cmmm;HS*)fFI$!3u(*[))QM%)*p$FI7$$"3m**\7y:A8hFI$!3lNkEz"**3(HFI7$$"34LLeR-/PiFI$!3TCT0J8m5=FI7$$"3-mmm"HZ_O'FI$!3$>xF%3,^bIF/7$$"3')***\PMaM\'FI$"3)oTpK,pNI"FI7$$"3oLL$eRh;i'FI$"3"3M#zMOR'y#FI7$$"3imm"zWo)\nFI$"3cN@y$e,B#RFI7$$"35L$eR(>(R"oFI$"3UrVm.e,-VFI7$$"3c*******\v!yoFI$"3Q&>?4[KJ`%FI7$$"3.m;/E!z@%pFI$"3)eF?8!=d/YFI7$$"3RLL3_DG1qFI$"3Z'oV;@%)3^%FI7$$"3Anm;/'*[MrFI$"3K1Uw=g0OQFI7$$"3;++DcmpisFI$"3B^64^pg$e#FI7$$"3%om;Hd)G&R(FI$"3!4CMXIrS`)F/7$$"3cLLe*[!)y_(FI$!3)H$3vS;no5FI7$$"3D++D1CZgwFI$!3;HPER3a"*GFI7$$"3%pm;HKkIz(FI$!3MBi:4>sHVFI7$$"3&)***\7Gg$fyFI$!3)fd*)fHzz#[FI7$$"3lLLeRilDzFI$!35'Gqh0Y![^FI7$$"35++v=U!)ezFI$!3N#[8!=x@O_FI7$$"3Wnm"z>_>*zFI$!3?'z7#GCou_FI7$$"3yML3x,5D!)FI$!3"H/B*Guni_FI7$$"3M++Dc"[#e!)FI$!3uxW4BM#**>&FI7$$"3#zm;H2S3>)FI$!33bxF1*zHX%FI7$$"3uLLe*)>VB$)FI$!3%)z([&ysl(*HFI7$$"3)om"H#o)fb%)FI$!3!o3ebkAP/"FI7$$"3.+++v`w(e)FI$"3)HJ-S#4$z7"FI7$$"3=L$3x1K*>()FI$"3;Q?1P%>4>$FI7$$"3KmmTg()4_))FI$"34.e<q94E[FI7$$"3+K3x1@==*)FI$"3S5piZ8w(R&FI7$$"3Z**\7`aE%)*)FI$"33Kex!464x&FI7$$"3J#3-j72t,*FI$"3JeC7E=SxeFI7$$"3#p;z%*z[.0*FI$"3,m")oI7[GfFI7$$"3w\ils/R$3*FI$"3=QU`6CGBfFI7$$"3hKL$e9Kk6*FI$"3GRuxHLZheFI7$$"3`n;aQ))f[#*FI$"3[XEeksWg]FI7$$"3n++DJbw!Q*FI$"3[uJewlCmMFI7$$"3f%3_+A:n^*FI$"3Eyc3Be8M7FI7$$"3smT&)3\m_'*FI$!3Q3$4)*QvlD"FI7$$"3j]il(f9')y*FI$!3edOm>jF5OFI7$$"3aM$ekGkX#**FI$!3?*>)Q'*eAVaFI7$$"3Sx$f38RD***FI$!38C(*\9>KjgFI7$$"3&=/EvR^g+"!#;$!3)evarnRhW'FI7$$"3"Q4Y(R,X45F_gl$!3cn(R#o-TUlFI7$$"3&f9m>))[G,"F_gl$!3C&4$4&H;Kd'FI7$$"35)>'=CwC;5F_gl$!3l.q5rP%y`'FI7$$"3C]iSmjk>5F_gl$!3],QFZdCOkFI7$$"3XekGN8CL5F_gl$!3VAH'Qhn+R&FI7$$"3%ommTIOo/"F_gl$!3,2;F%eE6X$FI7$$"3?]i:g2")e5F_gl$!3[;X5LVuK7FI7$$"3QLe9;_yq5F_gl$"3>ah-c,g&="FI7$$"3t;a8s'fF3"F_gl$"3*)Qou8')30NFI7$$"33+]7GTt%4"F_gl$"3BB7``^DLaFI7$$"3W$e9Te3n5"F_gl$"3ueX$Q-))3s'FI7$$"3zmT5SIo=6F_gl$"3k8jQi'4U>(FI7$$"3:]P4'\d18"F_gl$"3LO01uK=ynFI7$$"3]LL3_>jU6F_gl$"3Ky7.Mm$y]&FI7$$"3;vVt_@P\6F_gl$"3O)e%4Y^gmWFI7$$"3$oT&Q`B6c6F_gl$"3#Qu>kDhsB$FI7$$"3\ek.aD&G;"F_gl$"3=?eY)=:n'=FI7$$"3:+voaFfp6F_gl$"3T?V@yp%)zSF/7$$"3"=aQ`&HLw6F_gl$!3Qr%4@ad=3"FI7$$"3Z$e*)f:tI="F_gl$!3'HVLPO>Ra#FI7$$"38D1kcL")*="F_gl$!3.QUX$o>)>RFI7$$"3!om"HdNb'>"F_gl$!3g,x)>!>-a^FI7$$"36]PfeR.57F_gl$!3DoFEaTo-qFI7$$"3WLe*)fV^B7F_gl$!3$["QFY$RDy(FI7$$"3w;z>hZ*pB"F_gl$!3/AV[ymX\tFI7$$"3E++]i^Z]7F_gl$!3d7jxTyb[dFI7$$"3:+D1RICd7F_gl$!3:7w')G%H0d%FI7$$"3@+]i:4,k7F_gl$!3Kc'*=Fc!))>$FI7$$"3F+v=#zy2F"F_gl$!3jJfm3")\'o"FI7$$"3M++vomax7F_gl$!3Yk]LgLh%G*FL7$$"3S+DJXXJ%G"F_gl$"3^Tz-sh5>:FI7$$"3G+](=U#3"H"F_gl$"3j:8*>j1]3$FI7$$"3=+vV)H]yH"F_gl$"38p:$4$pwTXFI7$$"3C+++v"=YI"F_gl$"3cB(R">n5IeFI7$$"3=+]7GR:=8F_gl$"3;%[%)\0'p(p(FI7$$"39++D"o*oJ8F_gl$"3)=Ar#y0)\P)FI7$$"34+]PMaAX8F_gl$"3C*opRmzLt(FI7$$"3/++](=h(e8F_gl$"3X&)eJ"eTA&eFI7$$"39+]i!H$Gl8F_gl$"3IOxWpIvyXFI7$$"31++v$R0=P"F_gl$"337:'eTd^7$FI7$$"3)***\(o\F$y8F_gl$"3VD`')oz+W:FI7$$"33++++'\[Q"F_gl$!3G+)edt%yp5F/7$$"3=+]7.<P"R"F_gl$!3")>#zZpIqw"FI7$$"35++D1Q*yR"F_gl$!3)eM#\QDcuLFI7$$"3.+]P4fT/9F_gl$!3sEt'\@g%p[FI7$$"38++]7!Q4T"F_gl$!3_'>$)3RK`>'FI7$$"3:++v=A)RU"F_gl$!3Zi'>Zs;c9)FI7$$"3=+++Dk-P9F_gl$!39(o*R&=%*R#*)FI7$$"3?++DJ12]9F_gl$!3Wfw'))e#z(R)FI7$$"3A++]P[6j9F_gl$!3HlaKVrEDmFI7$$"3&f9m>`P!p9F_gl$!3V4HZ>)>'oaFI7$$"3'=HKkAg\Z"F_gl$!3`)yHZvMr8%FI7$$"3wP%)*3#H)3["F_gl$!3Pee)\BL/n#FI7$$"3\$ek`h0o["F_gl$!3g.Ug)zRD6"FI7$$"3AH2$)4$GF\"F_gl$"3MUy'4t/W*[F/7$$"37voH/5l)\"F_gl$"3F7Pa=yu'3#FI7$$"3.@Iw)ptX]"F_gl$"3!oa3Hg`/j$FI7$$"3wm"HKR'\5:F_gl$"3eX$QAugH2&FI7$$"3Re9;#yTB_"F_gl$"3)of!yhbQzuFI7$$"3-]P4rr=M:F_gl$"3*RwR_NMa+*FI7$$"3$f*)fb')4,a"F_gl$"3X.GjP#R>P*FI7$$"3%=/E+cKga"F_gl$"3Z*o(\KA>a%*FI7$$"3c(=#\a_&>b"F_gl$"35Xtfd=%zC*FI7$$"3ZL$e*[z(yb"F_gl$"3A3Hyl0vd()FI7$$"3AaQ`01#\c"F_gl$"3B7Aoq+DCyFI7$$"39v$4@Ej>d"F_gl$"3/Q)z`U>ha'FI7$$"31'*[o=f+z:F_gl$"3-:O$)zZ>w\FI7$$"3)pTg_d[ge"F_gl$"3@?i')HqJ!=$FI7$$"3!z$f$=B"4$f"F_gl$"3.%G;t/pXB"FI7$$"3$)e9T))Q8+;F_gl$!3;p&z)3h]zxF/7$$"3Rzp)\awrg"F_gl$!3l%H*Gs0oqFFI7$$"3K+Dc,#>Uh"F_gl$!3==r1DSKdYFI7$$"3C@!Q"e=E@;F_gl$!3xv&)e:**ebjFI7$$"3!=a8Z^/$G;F_gl$!3)R/PQg&y!z(FI7$$"3ti!*GrrMN;F_gl$!3W"yb'))R5**))FI7$$"3l$eky#)*QU;F_gl$!3mI)GgNg/j*FI7$$"3HWB:c6"fk"F_gl$!39'4\GN[M%)*FI7$$"3d/,W%[K%\;F_gl$!374KJAGv]**FI7$$"3'['ys7Q&Hl"F_gl$!3Ns[R'4o3&**FI7$$"3]Dc,T^Zc;F_gl$!3vUB'3ZWM%)*FI7$$"31Y6f(z<Nm"F_gl$!3ygt%f4%R5$*FI7$$"3*pmmTXg0n"F_gl$!3-<#Hpk%*=P)FI7$$"3@<H23l_w;F_gl$!35]#[?GmtG(FI7$$"33n"z>c#\#o"F_gl$!3\#\dn5"3rfFI7$$"3&pT&)ehe%)o"F_gl$!3Jq%*4-dkiWFI7$$"3#om"zpYU%p"F_gl$!3)HIiz'o%y!GFI7$$"3o;zpB2R+<F_gl$!3,n.KH1Ed5FI7$$"3"p;/wxcjq"F_gl$"3%zz&=W9&HN(F/7$$"38</^JGK7<F_gl$"3;7wF9rT9DFI7$$"3+nmT&)))G=<F_gl$"3/dG*R!3$[A%FI7$$"3(o"HKR\DC<F_gl$"3EMe;$y4J"eFI7$$"3um"HK*4AI<F_gl$"3&oSv><Y$HsFI7$$"3g;a8Zq=O<F_gl$"3)o9!)Q=?(G%)FI7$$"3$omT55`@u"F_gl$"31VXT1$>HP*FI7$$"30<z%\:>"[<F_gl$"3O-!))f@OJ+"F_gl7$$"3#p;a)3_3a<F_gl$"3D'oZQz=#Q5F_gl7$$"3'=H2eBoqv"F_gl$"3!QBnk7)zV5F_gl7$$"3z;/wi70g<F_gl$"3s;h?XzHT5F_gl7$$"3tTNr*GMIw"F_gl$"3Ey=y&p<2."F_gl7$$"3mmmm;t,m<F_gl$"39X">Lf>@,"F_gl7$$"3iiSmbs&Hx"F_gl$"3&GYY>QhjQ*FI7$$"3de9m%>(*)z<F_gl$"3huY#)3&QRD)FI7$$"3`a)eO8Poy"F_gl$"3;D#3U1)=pnFI7$$"37]ilsqx$z"F_gl$"3=1/7&*)>C*\FI7$$"3tXOl6qr+=F_gl$"3uv)['HAa'*HFI7$$"3oT5l]pl2=F_gl$"3972toRnS')F/7$$"3kP%['*)of9=F_gl$!3ke([n$HI;8FI7$$"3gLekGo`@=F_gl$!3;f(*\V:P`MFI7$$"3bHKknnZG=F_gl$!3A1VLHWEdaFI7$$"3:D1k1nTN=F_gl$!3ewaeeX@VsFI7$$"3v?!QckcB%=F_gl$!37'eeF/^^t)FI7$$"3r;aj%e'H\=F_gl$!3Y,cyy;%*o)*FI7$$"3m7GjBlBc=F_gl$!3unae_]^f5F_gl7$$"3i3-jik<j=F_gl$!3*=*)H<>>")3"F_gl7$$"3e/wi,k6q=F_gl$!3k#Q&Q6(y72"F_gl7$$"3=+]iSj0x=F_gl$!3F)z7'peY45F_gl7$$"3X/^ci$*>$)=F_gl$!3a&GW8.=3>*FI7$$"3P3_]%QU$*)=F_gl$!3(>e/<\r5)zFI7$$"3m7`W1a[&*=F_gl$!3@a$\o%)>Q]'FI7$$"3#pT&QG%G;!>F_gl$!3/kW7c^V1[FI7$$"3&3_D.Xrx!>F_gl$!3)oB(p_0uVHFI7$$"37DcEsW"R">F_gl$!3JO,'>9yBw*F/7$$"3SHd?%\d+#>F_gl$"3"[(z\?*f=."FI7$$"3KLe9;0?E>F_gl$"3i<*>$\is9IFI7$$"3gPf3QNMK>F_gl$"3mF^_)y"32\FI7$$"3(=/E+c'[Q>F_gl$"3p(*fMhcMYmFI7$$"3!e9m>eHY%>F_gl$"3umwB2squ")FI7$$"32]i!Rgs2&>F_gl$"3E$48&f#\5W*FI7$$"3Naj%ei:p&>F_gl$"3Tkz2&*eES5F_gl7$$"3FekyZ'eI'>F_gl$"35\*R^(om-6F_gl7$$"3e5lve,8m>F_gl$"3iNP38yZ?6F_gl7$$"3ailsp;?p>F_gl$"3_`')>6z6H6F_gl7$$"3]9mp!=tA(>F_gl$"3rL`Est\G6F_gl7$$"3#omm;pW`(>F_gl$"3)ez8)QCg=6F_gl7$$"3*Gc^.c%3#)>F_gl$"32y6FaO![1"F_gl7$$"3gek.HW#)))>F_gl$"3R;\,`!ppo*FI7$$"3Ia8s(Hkb*>F_gl$"3!HgB%>3'*Q$)FI7$$"3P]iSmTI-?F_gl$"3KLGe68ibmFI7$$"33Y64NS/4?F_gl$"3,#Hwi)R0-ZFI7$$"3!=/wP!Ry:?F_gl$"3$3!eYKjLaDFI7$$"3'y$4YsP_A?F_gl$"3`i[_h;alHF/7$$"3eLe9TOEH?F_gl$!31&)=.$4%\#)>FI7$$"3GH2$)4N+O?F_gl$!3%p())RVQz#>%FI7$$"3ODc^yLuU?F_gl$!3w3kt#ftmC'FI7$$"31@0?ZK[\?F_gl$!34t"eGA'Gi!)FI7$$"3y;a)e6Bi0#F_gl$!3b8_=XQ(oc*FI7$$"3%GJqX)H'H1#F_gl$!3g@fo)eo*p5F_gl7$$"3b3_D`Gqp?F_gl$!3Ca!QyKV99"F_gl7$$"3Bcwf(ysI2#F_gl$!39@mm'***\g6F_gl7$$"3F/,%>sUk2#F_gl$!36eF.bz6o6F_gl7$$"3I_DGcE")z?F_gl$!3+C>:R!*>k6F_gl7$$"3L+]i!f#=$3#F_gl$!3S"3F%f"f([6F_gl7$$"35DJXR0g*3#F_gl$!36J<!)z/0)3"F_gl7$$"3A]7G)[=g4#F_gl$!3"o]S]F'Q"))*FI7$$"3Lv$4rVOC5#F_gl$!3qw$Q>$ofC&)FI7$$"35+v$fQa)3@F_gl$!3`)R8E7cu&oFI7$$"3ADcwMBF:@F_gl$!3CQE[s8fQ\FI7$$"3M]Pf$G!p@@F_gl$!3bbRO2Q(e$GFI7$$"35v=UK#3"G@F_gl$!3u^=@()[:SiF/7$$"3A++D"=EX8#F_gl$"3H%*f/j#)3=;FI7$$"3MD"y+8W49#F_gl$"3$4[%==i<5QFI7$$"36]i!*y?OZ@F_gl$"3%RH"fPw\teFI7$$"3BvVtF+y`@F_gl$"3+[iUAXkLxFI7$$"3N+Dcwz>g@F_gl$"3mX/+TxBB$*FI7$$"3B](=U(Q.t@F_gl$"3)4F"yv;2Z6F_gl7$$"36+](=xpe=#F_gl$"3XDt%>FT,?"F_gl7$$"3Q/,>Gic#>#F_gl$"3<qW7*y'zf6F_gl7$$"3m3_]%oi#*>#F_gl$"3">&*zd!H5u5F_gl7$$"3d7.#39ff?#F_gl$"3MwOcA&pCY*FI7$$"3%oTNrfbE@#F_gl$"3'e!HJj)H2"yFI7$$"36@0X`?N>AF_gl$"3N<y&yz")*[eFI7$$"3.Dcw4&[gA#F_gl$"3y+vt=+r_OFI7$$"3IH23m\uKAF_gl$"3p`VbYY!oI"FI7$$"3dLeRA9WRAF_gl$!3=Tr@&eBx4"FI7$$"3%y$4ryy8YAF_gl$!3`T*yb;ysY$FI7$$"36Ug-NV$GD#F_gl$!3+\>d7UK4dFI7$$"3.Y6M"zI&fAF_gl$!3j`sA_h+OxFI7$$"3I]ilZsAmAF_gl$!3"[>f!zSfn%*FI7$$"3\ekGg,izAF_gl$!3BQzHW/cy6F_gl7$$"3-nm"H28IH#F_gl$!3M#elp-u&H7F_gl7$$"3qa8A5D;*H#F_gl$!3%>[.f-j))="F_gl7$$"3+Ug_Z>J0BF_gl$!3g0]!GC`*36F_gl7$$"3KH2$[Qh9J#F_gl$!3_Uz/r.mB**FI7$$"3)pTN@#3h<BF_gl$!3k*3Z6Kr$G%)FI7$$"3l/,Wf-wBBF_gl$!3sV4;B%o>l'FI7$$"3'>zWnp4*HBF_gl$!3do#Q:%*Q@l%FI7$$"3Fz%\S8fgL#F_gl$!3iOCd[*yS\#FI7$$"3%p;a8d3AM#F_gl$!3i5')y5_l$[#F/7$$"3ga)e'3!e$[BF_gl$"32!y0:.a8,#FI7$$"3">ajfW2XN#F_gl$"3$Q?DS;!y5UFI7$$"3AH#oK)olgBF_gl$"3b%p3*QoSxiFI7$$"3*o"Hd?j!oO#F_gl$"31P*\wT9H9)FI7$$"3c/w(yvbHP#F_gl$"3W2TmT1VX(*FI7$$"3(=H#=&>0"zBF_gl$"3u'R+)z%eJ5"F_gl7$$"3=zp[KYD&Q#F_gl$"3#)[:Q!oGe>"F_gl7$$"3%om"zpSS"R#F_gl$"3rZ"o_=<%\7F_gl7$$"3FD"yv1qYS#F_gl$"3<3"ed<&*\A"F_gl7$$"3q$ek`1OzT#F_gl$"3#e$e^z&yY,"F_gl7$$"3"H"yDk!pXU#F_gl$"3Q3#\E_?[[)FI7$$"37U5:j??JCF_gl$"3-c2Y5mO%\'FI7$$"3)4FW?1NyV#F_gl$"3m7<#\.]2D%FI7$$"3?+v$41oWW#F_gl$"3axbAB@<R=FI7$$"3TH2$)f55^CF_gl$!3>s+JlgH&['F/7$$"3FeRseStdCF_gl$!3KN(yMy#Q<JFI7$$"3\(=<w0nVY#F_gl$!3[&e6!e+"HZ&FI7$$"3q;/^c++rCF_gl$!3C];->'[Zi(FI7$$"3"fk.a0LwZ#F_gl$!3/@$[<`?,\*FI7$$"38voHagE%[#F_gl$!3q"R2u/-(*4"F_gl7$$"3M/,>`!**3\#F_gl$!3')[UY)z*p37F_gl7$$"3cLL3_?`(\#F_gl$!3#pr$QhEur7F_gl7$$"3Z3FW&p68^#F_gl$!3!\U0'4h0Z7F_gl7$$"3Q$3-)Q84DDF_gl$!3S61jI4\=5F_gl7$$"3%3x"[g6)>`#F_gl$!3U2;c-opz$)FI7$$"3Ie9;#)4()QDF_gl$!3q*>'[2p4DiFI7$$"3wX6%Q!3wXDF_gl$!3r!>'3-#R#4QFI7$$"3dL3_D1l_DF_gl$!3isNOHgAJ7FI7$$"3Ix1OOb4cDF_gl$"3\Qt(fQz8c)FL7$$"3R@0?Z/afDF_gl$"3))[K0au$HS"FI7$$"36l./e`)Hc#F_gl$"3,2J_:A82FFI7$$"3%)3-))o-VmDF_gl$"3Nqgltqq%)RFI7$$"3I'*)f04?Ld#F_gl$"3E&=zcVxuS'FI7$$"3w$eRA"*4-e#F_gl$"3ZpIa&z))4d)FI7$$"3Ar#>Rt*4(e#F_gl$"3+Im3i![&Q5F_gl7$$"3oe*)fb&*)Rf#F_gl$"3:R(Q(e>ax6F_gl7$$"38Y'ysPz3g#F_gl$"3>'zm6qk#o7F_gl7$$"3fL$e*)>pxg#F_gl$"3;Zj2W9)oI"F_gl7$$"35</,>Ww>EF_gl$"3!)fV*3NufC"F_gl7$$"3E+D1R'f<j#F_gl$"3'H7x1;"=I5F_gl7$$"3,U&)3\svPEF_gl$"3<uu9'=fur)FI7$$"3T$e9"f[vVEF_gl$"3EJXU#z!=eoFI7$$"3<D19pCv\EF_gl$"3XKO&**Q/<y%FI7$$"3#pmm"z+vbEF_gl$"3%)48&)3Hk_DFI7$$"3o3F>*oZ<m#F_gl$"3@?QCBU"[S#F/7$$"3V](=#*HXxm#F_gl$!3FPD=U8f#3#FI7$$"3$=zW#4HutEF_gl$!31eOY1%RRM%FI7$$"3fL3F>0uzEF_gl$!3;VD%3D`FZ'FI7$$"3MvoHH"Qdo#F_gl$!3gHDCv&pAS)FI7$$"3u;HKRdt"p#F_gl$!3l&[F[u'=25F_gl7$$"3]e*[$\Lt(p#F_gl$!35j[&f\(*G9"F_gl7$$"3D+]Pf4t.FF_gl$!3kY#\UjsIC"F_gl7$$"3E@I^U&3-r#F_gl$!3o?upC#4xI"F_gl7$$"3!>/^c7'o;FF_gl$!3hAMF,LyC8F_gl7$$"3ci!*y3P;BFF_gl$!3;L='4J0OH"F_gl7$$"3c$3F>HT'HFF_gl$!3@!\n?<X_@"F_gl7$$"3c/^1v)=ht#F_gl$!39OgT[c\#4"F_gl7$$"3@DJ?ekfUFF_gl$!3-7K-Lus(H*FI7$$"3'e9T8/u!\FF_gl$!3%e))\Pom&HtFI7$$"3'o;zWi^bv#F_gl$!3A&*=H07z"4&FI7$$"3(y=<w?H?w#F_gl$!3g_(e'3dklEFI7$$"3^3_v!z1&oFF_gl$!3'*RnfVh\$R"F/7$$"3;HK*QP%)\x#F_gl$"3))o[pWW6&R#FI7$$"3<]7.d>Y"y#F_gl$"3g_6`TNNX[FI7$$"3<r#p,aRzy#F_gl$"3PhE?Ok$>7(FI7$$"3#=H2L7<Wz#F_gl$"3J&**oiTh;9*FI7$$"3Z7`W1Z*3!GF_gl$"3`F"*\X+1$3"F_gl7$$"3ZLLe*Gst!GF_gl$"3Ns3^=3o77F_gl7$$"3?vozmU19GF_gl$"33rCa<xH+8F_gl7$$"3%pT5SCc2#GF_gl$"3KLh`$oduL"F_gl7$$"3KeRA@#[u#GF_gl$"3d1NgM*fEK"F_gl7$$"3/+vV)>ST$GF_gl$"3%[3'G_WUc7F_gl7$$"3yT5lv@$3%GF_gl$"33Xxz))QFT6F_gl7$$"3;$ekG:Cv%GF_gl$"3wBj<UTP;)*FI7$$"3*[7y+8;U&GF_gl$"3-4$>`r,o$yFI7$$"3jm;H2"34'GF_gl$"3o.qJM"\1b&FI7$$"3nP%)*e4aU'GF_gl$"3!)*\9g%e#*>VFI7$$"3O3_]%3+w'GF_gl$"3iqe.r/bYIFI7$$"30z>6tg%4(GF_gl$"3[x1miM"Hu"FI7$$"34](=<1#HuGF_gl$"3/a@)e!31<UF/7$$"39@bK]!Qw(GF_gl$!3-kMXOI.U!*F/7$$"3$=HK*QS)4)GF_gl$!3!y%\T'o%*=A#FI7$$"3^i!Rv-IV)GF_gl$!3)Rcm>ZA&=NFI7$$"3cLe9;gn()GF_gl$!3wqdhT3W"y%FI7$$"3Iv$fL*zO%*GF_gl$!340/.#o-t:(FI7$$"3-<Hdq*f5!HF_gl$!3"QoE"\U"pD*FI7$$"3SekyZ>v2HF_gl$!3%3hNeQQ)*4"F_gl7$$"39+++DRW9HF_gl$!3jMIKr"p8B"F_gl7$$"3?D19>2*4#HF_gl$!3Sk-,y5&QJ"F_gl7$$"3#*\7G8v`FHF_gl$!32'[T3E2vM"F_gl7$$"3)\(=U2V3MHF_gl$!3%)G1fl)\5L"F_gl7$$"30+Dc,6jSHF_gl$!3yg'o9)o0l7F_gl7$$"37DJq&*y<ZHF_gl$!3c([Rn)=&>:"F_gl7$$"3>]P%)*oCP&HF_gl$!3XC6kO&\"f**FI7$$"3DvV)R[r-'HF_gl$!3%4"))R9*zs-)FI7$$"3K+]7y#=o'HF_gl$!3meLycDg&z&FI7$$"3RDcEs]OtHF_gl$!3t0Z:/*>qM$FI7$$"3Y]iSm="*zHF_gl$!3!R^-4*4hDxF/7$$"3"GcwME&=$)HF_gl$"3#=[]!*HE.K&F/7$$"3<voag'ek)HF_gl$"3il4%=+1?$=FI7$$"3)y=<w0K(*)HF_gl$"3a**euVJB:JFI7$$"3C+voaa+$*HF_gl$"3W.^C#QT(pVFI7$$"3ID"G)[Ab**HF_gl$"3koyh5]9YnFI7$$"3,](oH/*41IF_gl$"3,Ao_G)zE())FI7$$"33v$4r$ek7IF_gl$"3Q\bd4u+n5F_gl7$$"3:++DJE>>IF_gl$"3W'pOz(z727F_gl7$$"3mP4@"*p_DIF_gl$"3&pqH4r^+I"F_gl7$$"3=v=<^8'=.$F_gl$"3F"Gg@8DxM"F_gl7$$"3%RM_6`G].$F_gl$"3+%=0c30SN"F_gl7$$"3q7G86d>QIF_gl$"30#\)\10Z[8F_gl7$$"3Y"G86*GOTIF_gl$"3OD_bax;J8F_gl7$$"3A]P4r+`WIF_gl$"3cvgo3gC-8F_gl7$$"3u(oa5Vk30$F_gl$"3rjhcLxk57F_gl7$$"3EDc,"z)>dIF_gl$"39="yU_ao2"F_gl7$$"3yil(4:LN1$F_gl$"3!*z+Iw_<b!*FI7$$"3I+v$4^n)pIF_gl$"39!3"z#=$)f-(FI7$$"3#yV)*3(=?wIF_gl$"31H."*>Bh^ZFI7$$"3Mv$f3BOD3$F_gl$"3CI')R,:F6BFI7$$"3'GJ?3fq))3$F_gl$!3">NcZLn-5#F/7$$"3Q]7y]\?&4$F_gl$!3%Ro7Z-JWs#FI7$$"3*y=U2JR:5$F_gl$!30nA#)[dJW^FI7$$"3TDJqqO(y5$F_gl$!3[w)[[?Q`Q(FI7$$"3$H1k1.3U6$F_gl$!3Ob]ZX;Qp$*FI7$$"35+]i!RU07$F_gl$!33wiMM"GF5"F_gl7$$"3#G"GQ<cdFJF_gl$!3?:/AYCiT7F_gl7$$"3?D19W)3Y8$F_gl$!3]:e-K$\sK"F_gl7$$"3QJ&>vXD"QJF_gl$!3JWn4.P%)[8F_gl7$$"3cP%)*32U;9$F_gl$!3zVY:i2$fN"F_gl7$$"3vVtF%oe^9$F_gl$!300&>u>M%[8F_gl7$$"3%*\il(Hv'[JF_gl$!3s+s7IZVE8F_gl7$$"3JiSTC&3d:$F_gl$!3wb!yLBG+C"F_gl7$$"3/v=<^<uiJF_gl$!3U'3PxyA/5"F_gl7$$"3x(oHz(\xpJF_gl$!3)HV#H8#[h8*FI7$$"39+vo/#3o<$F_gl$!3)[F0=>yi(oFI7$$"3K1k1=[K!=$F_gl$!3!fYCvY/#HcFI7$$"3^7`WJ9%Q=$F_gl$!3$H9/B>t;K%FI7$$"3q=U#[/et=$F_gl$!3FK+u.$fx'HFI7$$"3CDJ?eY(3>$F_gl$!3N!R;W6O?e"FI7$$"3yJ?er7R%>$F_gl$!3W3!)\wE=%z"F/7$$"3'z$4'\)y!z>$F_gl$"3KO^it*)*\A"FI7$$"3:W)R$)\C9?$F_gl$"3kbS8rB5;EFI7$$"3M](=<6T\?$F_gl$"3yY,HMN#*yRFI7$$"3_cw4DxX3KF_gl$"3[)G%zl,!))H&FI7$$"3rilZQV(>@$F_gl$"3x4H#3*R`hlFI7$$"3*)oa&=&4\:KF_gl$"3-<1zmOa`xFI7$$"33vVBlv+>KF_gl$"3J[..D5,i))FI7$$"3X(=#*>zSgA$F_gl$"3E+vQB!o"y5F_gl7$$"3#)***\(=S2LKF_gl$"3Q\I3S\#QA"F_gl7$$"3%>H2eo$RRKF_gl$"3]<i&3X;+J"F_gl7$$"3O$ekGN8dC$F_gl$"3y+'yz#fx]8F_gl7$$"3rGKR'=t)[KF_gl$"3G+$o%Q"=ON"F_gl7$$"3xu=#*>I._KF_gl$"3ImI%\L/ZM"F_gl7$$"3$3_]M&G>bKF_gl$"3G')*)e'*R6C8F_gl7$$"3*o;zpo_$eKF_gl$"3_Q!>.6G?H"F_gl7$$"3Iek.aBnkKF_gl$"3whYUc2f%>"F_gl7$$"3r\P4@?*4F$F_gl$"3O`t/c#)yb5F_gl7$$"3%=/^")o6tF$F_gl$"3b@mM?e]/))FI7$$"3DL$3_NJOG$F_gl$"3=OjJ&QMnu'FI7$$"3mCcEA5&**G$F_gl$"31XMw=51cWFI7$$"3y;HK*oqiH$F_gl$"3mG/KNv-7?FI7$$"3>3-Qc.f-LF_gl$!3ybL:1OS0]F/7$$"3g*\PM-5*3LF_gl$!3#Q5$y"\![%*HFI7$$"3s"z%\!pH_J$F_gl$!3<zHS^8K$Q&FI7$$"39$3_vN\:K$F_gl$!3;W%=5s$G%e(FI7$$"3bu$4Y-pyK$F_gl$!3P)zg:X_6_*FI7$$"3nmmm"p)=MLF_gl$!36"Q8m'=p76F_gl7$$"3')\i:&GO4M$F_gl$!3U4>&)z\NT7F_gl7$$"3.LekyQoZLF_gl$!3d#3h">."4K"F_gl7$$"3)\i!Rvw0^LF_gl$!3gmhSA4AT8F_gl7$$"3$pTN@ZJWN$F_gl$!3+\*)zG"[#[8F_gl7$$"3()3-))o_!yN$F_gl$!3N4=;%3F>M"F_gl7$$"36+]il!z6O$F_gl$!3[7LSR_KA8F_gl7$$"3H$e9"fm#zO$F_gl$!3/HK+t[?W7F_gl7$$"3=nTg_UnuLF_gl$!3HU3G[I,<6F_gl7$$"3O]P4Y=U"Q$F_gl$!3"**G#yIP8e%*FI7$$"3aLLeR%p")Q$F_gl$!3D'HguV_SP(FI7$$"3s;H2Lq"\R$F_gl$!3b9"o6-N0+&FI7$$"3!**\ilik;S$F_gl$!3aV`f0JgJCFI7$$"3&=H2LUQ]S$F_gl$!3)=$H%3cPa5"FI7$$"3!Q3_+A7%3MF_gl$"3\_x(4Nr2J#F/7$$"3uvoz;gy6MF_gl$"3q_-[w&*pk:FI7$$"3)pmTN")f^T$F_gl$"3Xsrj-IA#)GFI7$$"3;]7.2u!>U$F_gl$"3.b\&>!H5<aFI7$$"30M3_+]lGMF_gl$"3q^Dv1%yct(FI7$$"3C</,%f-aV$F_gl$"3J6j6hnbY(*FI7$$"3U++](=]@W$F_gl$"3!o)4kZ(fq8"F_gl7$$"3@Y645XE[MF_gl$"3P#*yAlVWX7F_gl7$$"3+#H#oK)yVX$F_gl$"3c%fH![QK88F_gl7$$"3aky(R*fVdMF_gl$"3WZ&QY)RMJ8F_gl7$$"3zPMFbJ\gMF_gl$"3M+q@*\L&Q8F_gl7$$"306!plJ]NY$F_gl$"3sxcu6#R[L"F_gl7$$"3f$ekyZ2mY$F_gl$"3Mz**QTlH?8F_gl7$$"3QHdX+=ssMF_gl$"3hu`\8![#f7F_gl7$$"3<vo/Bh$)yMF_gl$"335$fzt7u:"F_gl7$$"3(4-QcW]\[$F_gl$"3g0%[+7Q"=5F_gl7$$"3wm"H#oZ1"\$F_gl$"3k2]!46S)f%)FI7$$"3c7.#34zr\$F_gl$"3=.)*[EEtlkFI7$$"3Ne9T8MH.NF_gl$"31&)4_Y(ySE%FI7$$"39/E+OxS4NF_gl$"3U;Om`vcE>FI7$$"3$*\Pfe?_:NF_gl$!3/*['R>rz2ZF/7$$"3s&*[="QO;_$F_gl$!3B"\X,%[3]GFI7$$"3_Tgx.2vFNF_gl$!3sh.>>a9M^FI7$$"3K(=nj-lQ`$F_gl$!3`j^]?F%*[sFI7$$"35L$e*[$z*RNF_gl$!3wURlRJ/E"*FI7$$"3Y(oa&=RmYNF_gl$!3M**)z%)=&\$3"F_gl7$$"3"=/^")[[Lb$F_gl$!3g*G8HPr@@"F_gl7$$"3X&RZx0L+c$F_gl$!3]*317q-PH"F_gl7$$"3!)\PMFwrmNF_gl$!3gOqKoY*\K"F_gl7$$"3:/,%p>-Md$F_gl$!3*=))>r'f!\I"F_gl7$$"3zdk`mn3!e$F_gl$!3:)pTM+!HM7F_gl7$$"397G8O8x'e$F_gl$!3gv&pS))ef6"F_gl7$$"3]m"Hd!fX$f$F_gl$!3QrCd%)QrX&*FI7$$"3%3_D`ZS,g$F_gl$!3#>Og#*)Q\kvFI7$$"3>v=#\/Dog$F_gl$!3;i%GRf*H$H&FI7$$"3aH#=Xh4Nh$F_gl$!3eSm%[-H1#GFI7$$"3*Qe9T=%>?OF_gl$!3EOAfOKbECF/7$$"3rgF"*ok`BOF_gl$"3wVPmK`ea5FI7$$"3CQ4r`(yoi$F_gl$"3gNn^c!=0M#FI7$$"3x:"4&Q5AIOF_gl$"3f:h>&paEg$FI7$$"3g#H2LKjNj$F_gl$"3kWC=4)[(G[FI7$$"3CYO!H*yCSOF_gl$"3!4.i"QCuDrFI7$$"3e++]iC$pk$F_gl$"3GTOW3JyU"*FI7$$"30![\:7AKl$F_gl$"3bV=W^"H:2"F_gl7$$"3")e*)f!y6&fOF_gl$"3A')3<yhv">"F_gl7$$"3dP%['R9!em$F_gl$"3>^)yt(H*3F"F_gl7$$"3.<zp)4"4sOF_gl$"3-0Bza9H18F_gl7$$"3Evoz;/n%o$F_gl$"3q.Q(ei_GC"F_gl7$$"3[Le*[t\sp$F_gl$"3s68A>Ko55F_gl7$$"3&HJXRRRNq$F_gl$"3K+y:yo'eS)FI7$$"3r"z%*H0H)4PF_gl$"3]5AT3Sf>kFI7$$"3ZqU/7(=hr$F_gl$"3d=/hR;s;UFI7$$"3%*\P4r$3Cs$F_gl$"3AG%>nKsK(=FI7$$"3SHK9I!)pGPF_gl$!3(4D#f[OV+`F/7$$"3;3F>*o()\t$F_gl$!3^vBBO(41"HFI7$$"3#p=U#[tFTPF_gl$!3`m5<h"\n=&FI7$$"3Rm;H2qcZPF_gl$!3Bv>Ciw_!G(FI7$$"3I]7G8:9aPF_gl$!3+U$p+@#p'>*FI7$$"3]L3F>grgPF_gl$!31HYiZgUw5F_gl7$$"3q;/ED0HnPF_gl$!3S$>")yQ=D>"F_gl7$$"3!****\7.lQx$F_gl$!3,N^LH#zOE"F_gl7$$"3]"zWUG_rx$F_gl$!3$))pV9KP:G"F_gl7$$"35$eRs`R/y$F_gl$!3f$Rx7OOtG"F_gl7$$"3ruVB!zEPy$F_gl$!3j%>vL*[."G"F_gl7$$"3Jm"HK/9qy$F_gl$!3#fE*=L`qi7F_gl7$$"3]\(=#\&)e$z$F_gl$!3u#>)*o0:3>"F_gl7$$"3UL$3_0j,!QF_gl$!3pi'4UBlW2"F_gl7$$"3L<z>hvt1QF_gl$!3N`RcxN<"=*FI7$$"3`+v=n?J8QF_gl$!3W#))[[FNsF(FI7$$"3t$3xJd'))>QF_gl$!3H8m)za'*\5&FI7$$"3%pmm"z5YEQF_gl$!3YtxDNq^YFFI7$$"39]i:&eNI$QF_gl$!3=4NA!ROl!HF/7$$"3MLe9"45'RQF_gl$"3+4s$R#4Hq@FI7$$"3a;a8(f%=YQF_gl$"31xO'[@TSa%FI7$$"3X+]7."fF&QF_gl$"3/>YiyH"=u'FI7$$"3&[5SW)o=fQF_gl$"3kNh'3-+<k)FI7$$"3a3_vlYhlQF_gl$"3u3jX.'[F-"F_gl7$$"3$HJqqWU?(QF_gl$"3#z.c\V4V9"F_gl7$$"3L<aQG-ZyQF_gl$"3."*4-^geC7F_gl7$$"3<pH/>To")QF_gl$"36bOC>UJ[7F_gl7$$"3-@0q4!)*[)QF_gl$"3\Ei!f2.3E"F_gl7$$"3dt!e.!>6))QF_gl$"3l,">fUa>E"F_gl7$$"3UDc,"zD8*QF_gl$"3ujw(49s<D"F_gl7$$"3#)H2LsNv(*QF_gl$"3K;4=&fIz>"F_gl7$$"3]Lek`8=/RF_gl$"3g!Q%yQ<K,6F_gl7$$"3=P4'\841"RF_gl$"3&oOYDOu^l*FI7$$"3eTgF;p.<RF_gl$"3r?q"*Q.'[&zFI7$$"3)f9"f(pkM#RF_gl$"3"=1u>n/T(fFI7$$"3m\i!*yC*)HRF_gl$"3VAH,;Aj%y$FI7$$"31a8Ag-KORF_gl$"3LH_UXMYl9FI7$$"3Yek`T![F%RF_gl$!3'QgNCw0%***)F/7$$"3:i:&G#e<\RF_gl$!3or/$e6&oEKFI7$$"3amm;/OgbRF_gl$!37E"[e7#\JaFI7$$"3B7y]&*GLiRF_gl$!3ot9O-)RN_(FI7$$"3ie*[o=i!pRF_gl$!3cX&RuPuUJ*FI7$$"3I/,>y9zvRF_gl$!3@"4@"oqUt5F_gl7$$"3)*\7`p2_#)RF_gl$!3ma"*\2u)G<"F_gl7$$"3ZA=?:a)e)RF_gl$!3N.Dt@WT07F_gl7$$"3n&Rs31]#*)RF_gl$!3mI]-m0.E7F_gl7$$"3')oHa1Zh#*RF_gl$!3kr)GU%3bM7F_gl7$$"3MTN@_$zf*RF_gl$!3ig*eBt44B"F_gl7$$"3u(oaNk3F+%F_gl$!3&zHy/@![(="F_gl7$$"3ULe*[$zV4SF_gl$!3#=[$e3af(4"F_gl7$$"35zpBEs;;SF_gl$!3#p_K@k"G\'*FI7$$"3]D"yv^'*G-%F_gl$!3%Hx$))*H2#[zFI7$$"3=r#>*3eiHSF_gl$!3OH6&zW&pSfFI7$$"3'oTg-5bj.%F_gl$!3O\tOcY`1PFI7$$"3ai:g"R%3VSF_gl$!3^]$4(fL;M8FI7$$"3B3F%Ho8)\SF_gl$"3P+:J'oMG3"FI7$$"3iaQGuHacSF_gl$"33i*f]:E%\MFI7$$"3I+]ilAFjSF_gl$"3%fb]Z**oGn&FI7$$"3nq<)HP`(pSF_gl$"3ao,nzv%yf(FI7$$"3vT&Q.[Mi2%F_gl$"34W8d!)4.S#*FI7$$"3#GJ&p(e:F3%F_gl$"3A"=cm/_S0"F_gl7$$"3!R3_]p'>*3%F_gl$"3K0Vp^kIX6F_gl7$$"3Wp/t[sV#4%F_gl$"3i$QnssF`<"F_gl7$$"3)\&)3C!yn&4%F_gl$"3uOCvo/d%>"F_gl7$$"3_Ss3c$=*)4%F_gl$"3'H*4X))o(G?"F_gl7$$"3MDcw4*e@5%F_gl$"3%o@NZV*=+7F_gl7$$"3q&RAr,S'3TF_gl$"3g^#)=9^5i6F_gl7$$"3ym"zW7@^6%F_gl$"3iH1s'[_=3"F_gl7$$"3'y$f$=B-;7%F_gl$"3I0%H0(Q)\i*FI7$$"3%*3F>RL3GTF_gl$"34r)>#QVC&3)FI7$$"3,![\lWkX8%F_gl$"3#zV&><reciFI7$$"3Q]i!RbX59%F_gl$"3Hr@#))HDm?%FI7$$"3u?IEhm_ZTF_gl$"3d:&)>-?!3,#FI7$$"3#=z>'ox+aTF_gl$!3_.&ylf*)Q]#F/7$$"3!Hcwf())[gTF_gl$!3%H>\l.dV\#FI7$$"3(RLLL)*pp;%F_gl$!3YMaN**\VRYFI7$$"324Fp^yftTF_gl$!3[qhA1B")\mFI7$$"3<%3_+sD-=%F_gl$!3-&eJs,(f*R)FI7$$"3Ff9T)e`o=%F_gl$!3Q-evwZ8B)*FI7$$"3mL3xc9[$>%F_gl$!3(p>`cCXn3"F_gl7$$"303-8D$4,?%F_gl$!30;31gIU\6F_gl7$$"3:$e*[$>Pn?%F_gl$!3ge"4/"47o6F_gl7$$"3De*[=1lL@%F_gl$!3KG#HwX(HU6F_gl7$$"3NL$3-$H**>UF_gl$!3#)zw%p;5J2"F_gl7$$"3X3xc)z?mA%F_gl$!3$p;![bakL'*FI7$$"3b$3Fpm[KB%F_gl$!3P3$*y]n+u")FI7$$"3lekGNl()RUF_gl$!3c(3%=wh@4kFI7$$"3vLek.W]YUF_gl$!3hr'G(yZq2WFI7$$"3&)3_+sA8`UF_gl$!3ASx20%[mC#FI7$$"3&Rek.9g(fUF_gl$!381S:X['*))*)!#?7$$"30fRs3!)QmUF_gl$"3'4>XhL_(>AFI7$$"3WLL3xe,tUF_gl$"3:."[>AZZN%FI7$$"3![NYL'))ezUF_gl$"33-yw<Yy*H'FI7$$"3Xv$4'\=;'G%F_gl$"3NodcZg"4+)FI7$$"35'Rse$[t#H%F_gl$"3svPu3zX&R*FI7$$"3w;a8AyI*H%F_gl$"3#H=#)[A[K/"F_gl7$$"3TP%)R33)eI%F_gl$"3)yD(zaxY26F_gl7$$"3xe9m%z`CJ%F_gl$"33#4Ee/p*H6F_gl7$$"39![C4yE!>VF_gl$"3#*)pix-!456F_gl7$$"3z+v=n(*fDVF_gl$"3!p1]q%*f([5F_gl7$$"3W@0X`F<KVF_gl$"3;q2d%*fd%[*FI7$$"35UNrRduQVF_gl$"3yWNQ0d6J")FI7$$"3vil(fs=`M%F_gl$"3TrK%*Q[YzkFI7$$"36%eRAr"*=N%F_gl$"3Q>AH-F"Gf%FI7$$"3Z0E])pk%eVF_gl$"3dX!4=[sGa#FI7$$"38Ecw%oP]O%F_gl$"3#f$oT"\G:2%F/7$$"3yY'G5n5;P%F_gl$!3WU9)ztvRt"FI7$$"3Vn;HdO=yVF_gl$!31"GK`))3.!QFI7$$"3pQM-\NA%Q%F_gl$!3it.2H2%pc&FI7$$"3C4_vSME!R%F_gl$!3S&p()41j*\rFI7$$"3!)zp[KLI'R%F_gl$!3x9u5_G3+&)FI7$$"31^(=UAVBS%F_gl$!3sn/j1gfv&*FI7$$"3h@0&f6$Q3WF_gl$!3ht<qGwOM5F_gl7$$"3<#H#o2IU9WF_gl$!3.'p^FqP"y5F_gl7$$"3!y<[N&HW<WF_gl$!3RrjH(3/s3"F_gl7$$"3VjST**GY?WF_gl$!3N>*[u]Jw3"F_gl7$$"31\*z_%G[BWF_gl$!30P85/fVz5F_gl7$$"3)R$e9"z-lU%F_gl$!3g7()=i;qi5F_gl7$$"3a/w(GoUDV%F_gl$!3J&>$GW:H/5F_gl7$$"3!eP4Yd#eQWF_gl$!3%)=,-1^+W"*FI7$$"3NY6MmCiWWF_gl$!3:G`hax:gzFI7$$"3!p"H2eBm]WF_gl$!3c%*4&fcK,`'FI7$$"3<)o/)\AqcWF_gl$!3=Da>pnI+\FI7$$"3sek`T@uiWF_gl$!3P$Q")ywqJ7$FI7$$"3FH#oK.#yoWF_gl$!3.keoBijb7FI7$$"3`+++D>#[Z%F_gl$"3[Zf(e>$)yU'F/7$$"3">/EDKW<[%F_gl$"3[rwx4s(*yFFI7$$"3+%3_+sm')[%F_gl$"3q(z0u^O#)y%FI7$$"35E"yv6*e&\%F_gl$"3D&GBKChye'FI7$$"3ZnT5::^-XF_gl$"3**Q)y$R/J/")FI7$$"3B]i:5jN;XF_gl$"3o`<Kxio05F_gl7$$"3qL$3_5,-`%F_gl$"39IGq&zGT."F_gl7$$"3zvVt-N7PXF_gl$"3?d"QUFP"Q)*FI7$$"3<</E+f/WXF_gl$"3I`)3GNe*H*)FI7$$"3beky(Ho4b%F_gl$"3.gT5EbzcwFI7$$"3$**\7`p!*yb%F_gl$"3'*)R?A&RitgFI7$$"3JT&QG48[c%F_gl$"3P;#pAewzC%FI7$$"3S$ek.\N<d%F_gl$"3h1$3u<iqD#FI7$$"3\D1*y)ylyXF_gl$"3pB^1VT(\%=F/7$$"3(om;aG!e&e%F_gl$!3!GT9z\3K)=FI7$$"3YekGg<x"f%F_gl$!3Pp9uIqFeOFI7$$"31]i:NK'zf%F_gl$!3"[B*)G8v@I&FI7$$"3kTg-5Z:/YF_gl$!3J"p'z#Q()4w'FI7$$"3BLe*[=Y.h%F_gl$!3_4#HH'=D()zFI7$$"3U;ajM"HFi%F_gl$!3C()G3;Mb$f*FI7$$"3J+]P%37^j%F_gl$!3Q-!)G*fx>#**FI7$$"3?%e9T.&\ZYF_gl$!3a(*)e&*\6Q%*)FI7$$"3QnT&Q)z()fYF_gl$!3OyRbWcf-oFI7$$"3)*eRse%pgm%F_gl$!3!Gb9!=54$Q&FI7$$"3d]PfL4EsYF_gl$!3;7Nl<PD$z$FI7$$"3;UNY3CXyYF_gl$!370`&3(R#p3#FI7$$"3vLLL$)Qk%o%F_gl$!3c9<qGM*\@$F/7$$"3)H19pGX7p%F_gl$"3\?:4@kXf:FI7$$"3?#z%\!pYyp%F_gl$"3.b"G`5"[pLFI7$$"3U@b2%4[Wq%F_gl$"3/2RrXNpS]FI7$$"3l]il(\\5r%F_gl$"3zs))>!=)*3^'FI7$$"354x"[I_Us%F_gl$"3?PFk*R7:k)FI7$$"3cn"z>6but%F_gl$"3Kz_O*p")pX*FI7$$"3,E19>zl]ZF_gl$"3=te(p#RG`))FI7$$"3Y%3-jsgQw%F_gl$"32RPY]@gRpFI7$$"3p8G))H@YqZF_gl$"3qPv#fCL)zbFI7$$"3"HajM`jqx%F_gl$"3!G]1r9W">SFI7$$"3VrU/P\m$y%F_gl$"3T>@'RAfyJ#FI7$$"3m+]iSjE!z%F_gl$"3["Q@K!R&>T&F/7$$"3+v=<EZe'z%F_gl$!3&**Qr(Qh[n6FI7$$"3/](=<6.H![F_gl$!3U,%\Tp=T#GFI7$$"34DcE(\@#4[F_gl$!3$e^>#Q<urVFI7$$"39+D"G))Rb"[F_gl$!3gChP'Hivv&FI7$$"3C]i!Rlw"G[F_gl$!3:QeA^v0kyFI7$$"3M+++DM"3%[F_gl$!36Td(ze)>n))FI7$$"3W]P4'>]M&[F_gl$!3U59=oV[X')FI7$$"3a+v=np3m[F_gl$!3sc(4!R-zYsFI7$$"3evVt_`Ss[F_gl$!3A<GL#)pglhFI7$$"3j]7GQPsy[F_gl$!3WoU0^ERz[FI7$$"3oD"GQ7U])[F_gl$!3?f-^F_;MMFI7$$"3u+]P40O"*[F_gl$!3/!\")Hl56)=FI7$$"3Gj!RvZ]")*[F_gl$!33N*px(*3Ha"F/7$$"3#e7.dWS\!\F_gl$"3C$HC.-/Yc"FI7$$"3O)=nQTI<"\F_gl$"3V>S$R#G,2KFI7$$"3!4DJ?Q?&=\F_gl$"3jp#zue#*zq%FI7$$"3*fPf$=.5K\F_gl$"38!>I-WR"fqFI7$$"3P+voa-oX\F_gl$"3KaX=(\;6E)FI7$$"3$4`p(Q_2\\F_gl$"3mSqm$zlvN)FI7$$"3?i:&GAqC&\F_gl$"3l3s&[Q>*p$)FI7$$"3Z$fLp?le&\F_gl$"3Ab6)3E:%)H)FI7$$"3uCc,">g#f\F_gl$"3e%)oMTD8W")FI7$$"3H(oz"f,0m\F_gl$"3s6?bE%ecf(FI7$$"3$)\PMF,%G(\F_gl$"3FOr4S()>\nFI7$$"3P7y]&4I'z\F_gl$"3jLg<[[:TcFI7$$"3#\(=nj+U')\F_gl$"30y&)pp%o!=VFI7$$"3YPf$=.5K*\F_gl$"3NQL!4>pY$GFI7$$"#]F+$"3/!)*)GD1h^7FI-%&COLORG6&%$RGBG$F+!""F[gxF[gx-F&6$7SF)7$FG$"3O#Q,1_4_Q(F/7$Fao$"3COqcTuRz8FI7$Fiq$"37%>5C([N'4#FI7$Fat$"3SVbb[=/7GFI7$Fcw$"3i1!R#p%)G;NFI7$Fez$"3@yTX4iHgTFI7$Fg]l$"3-pRaiwN;[FI7$Fcal$"3Ql>&f(f^"[&FI7$F_el$"3k8PI;=?HhFI7$F\il$"3_po[&*)Rvx'FI7$Fd[m$"3_1y.`51KtFI7$F`_m$"3=<"41fMh$zFI7$F\cm$"3<xPzZ[Z>&)FI7$Fhfm$"3%e#4,:a-e!*FI7$F^[n$"3%>OHv**ed_*FI7$Fh`n$"3U3kq*z-a+"F_gl7$Fbfn$"3)fSyQ@kw/"F_gl7$Fb[o$"3uJ#G"3e"Q4"F_gl7$F\ao$"3uw'G_tf=8"F_gl7$Fffo$"3#=o9([CXq6F_gl7$F\[p$"3!*=)y)o7//7F_gl7$Fb_p$"3I[%)H3NqN7F_gl7$Fbdp$"3(GQX_Te;E"F_gl7$Fhhp$"3RqbrL-B'G"F_gl7$Fh]q$"3%fP,jp=zI"F_gl7$F^bq$"3?a!G'*QmNK"F_gl7$F^gq$"3Z.!\sYVqL"F_gl7$Fb]r$"3e_IoAk>Z8F_gl7$F\cr$"3!)="pNr$R`8F_gl7$Ffhr$"3k(3)3+r&eN"F_gl7$F^`s$"3!GQ$>.S^a8F_gl7$Fhes$"3nxn_r+l\8F_gl7$F\\t$"3=+pF3+lS8F_gl7$Ffat$"3)GV;(*p?"H8F_gl7$F`gt$"3c0f@>#zGJ"F_gl7$Ff[u$"3Y$*oAb(oTH"F_gl7$F`au$"3)eA0V(*46F"F_gl7$Fjfu$"3LJxS#em^C"F_gl7$Fd\v$"3QrRLw/[97F_gl7$F^bv$"3"3j`gQ)f"="F_gl7$F_gv$"3]_huqzoW6F_gl7$F_\w$"3mu/T%G0\5"F_gl7$Fiaw$"3lZ1&*pMll5F_gl7$F_fw$"3p9<1THh<5F_gl7$F[jw$"3%z+3L<q*>(*FI7$Fg]x$"3,Q`B5aP2#*FI7$Fcax$"3WiYJp2p#p)FI7$Fcfx$"3%e6B-`w[6)FI-Fhfx6&Fjfx$"#5F\gxF[gxF[gx-F&6$7SF)7$FG$!3O#Q,1_4_Q(F/7$Fao$!3COqcTuRz8FI7$Fiq$!37%>5C([N'4#FI7$Fat$!3SVbb[=/7GFI7$Fcw$!3i1!R#p%)G;NFI7$Fez$!3@yTX4iHgTFI7$Fg]l$!3-pRaiwN;[FI7$Fcal$!3Ql>&f(f^"[&FI7$F_el$!3k8PI;=?HhFI7$F\il$!3_po[&*)Rvx'FI7$Fd[m$!3_1y.`51KtFI7$F`_m$!3=<"41fMh$zFI7$F\cm$!3<xPzZ[Z>&)FI7$Fhfm$!3%e#4,:a-e!*FI7$F^[n$!3%>OHv**ed_*FI7$Fh`n$!3U3kq*z-a+"F_gl7$Fbfn$!3)fSyQ@kw/"F_gl7$Fb[o$!3uJ#G"3e"Q4"F_gl7$F\ao$!3uw'G_tf=8"F_gl7$Fffo$!3#=o9([CXq6F_gl7$F\[p$!3!*=)y)o7//7F_gl7$Fb_p$!3I[%)H3NqN7F_gl7$Fbdp$!3(GQX_Te;E"F_gl7$Fhhp$!3RqbrL-B'G"F_gl7$Fh]q$!3%fP,jp=zI"F_gl7$F^bq$!3?a!G'*QmNK"F_gl7$F^gq$!3Z.!\sYVqL"F_gl7$Fb]r$!3e_IoAk>Z8F_gl7$F\cr$!3!)="pNr$R`8F_gl7$Ffhr$!3k(3)3+r&eN"F_gl7$F^`s$!3!GQ$>.S^a8F_gl7$Fhes$!3nxn_r+l\8F_gl7$F\\t$!3=+pF3+lS8F_gl7$Ffat$!3)GV;(*p?"H8F_gl7$F`gt$!3c0f@>#zGJ"F_gl7$Ff[u$!3Y$*oAb(oTH"F_gl7$F`au$!3)eA0V(*46F"F_gl7$Fjfu$!3LJxS#em^C"F_gl7$Fd\v$!3QrRLw/[97F_gl7$F^bv$!3"3j`gQ)f"="F_gl7$F_gv$!3]_huqzoW6F_gl7$F_\w$!3mu/T%G0\5"F_gl7$Fiaw$!3lZ1&*pMll5F_gl7$F_fw$!3p9<1THh<5F_gl7$F[jw$!3%z+3L<q*>(*FI7$Fg]x$!3,Q`B5aP2#*FI7$Fcax$!3WiYJp2p#p)FI7$Fcfx$!3%e6B-`w[6)FIF``y-%+AXESLABELSG6$Q"t6"Q!F[jy-%%VIEWG6$;F[gxFcfx;$!2%)\*R>l;59!#:$"2C%HLdG459Fdjy

For NiMvJSZvbWVnYUciIiQ= we getdsolve({D(D(x))(t)+9*x(t)=4*cos(3*t),x(0)=0,D(x)(0)=0},x(t));

NiMvLUkieEc2IjYjSSJ0R0YmLCQqJi1JJHNpbkc2JEkqcHJvdGVjdGVkR0YuSShfc3lzbGliR0YmNiMsJEYoIiIkIiIiRihGMyMiIiNGMg==

sol(t):=2/3*sin(3*t)*t;

NiM+LUkkc29sRzYiNiNJInRHRiYsJComLUkkc2luRzYkSSpwcm90ZWN0ZWRHRi5JKF9zeXNsaWJHRiY2IywkRigiIiQiIiJGKEYzIyIiI0Yy

env(t):=2/3*t;

NiM+LUkkZW52RzYiNiNJInRHRiYsJEYoIyIiIyIiJA==

plot([sol(t),env(t),-env(t)],t=0..25,color=[black,red,red]);

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