{VERSION 5 0 "SUN SPARC SOLARIS" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 " " 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "restart: with(plots) : with (linalg): with(DEtools):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warnin g, the name changecoords has been redefined\n" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and trace have been red efined and unprotected\n" }}{PARA 7 "" 1 "" {TEXT -1 45 "Warning, the \+ name adjoint has been redefined\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "First we'll set some of the parameters." }{MPLTEXT 1 0 1 " " } {TEXT -1 53 "You'll have to go back and change these values later." }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "k := 25;\ng := 9.8;\nc := . 05;\nf := t -> 0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"kG\"#D" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG$\"#)*!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG$\"\"&!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"fG\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "Now we define the th ree main equations." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 186 "ode1 := diff(x(t),t,t) + c*diff(x(t),t) + k*sin(x(t) )*cos(x(t)) = f(t);\node2 := diff(y(t),t,t) + c*diff(y(t),t) + (k/3)*y (t) = g;\node3 := diff(x(t),t,t) + c*diff(x(t),t) + k*x(t) = f(t);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ode1G/,(-%%diffG6$-%\"xG6#%\"tG-%\" $G6$F-\"\"#\"\"\"*&$\"\"&!\"#F2-F(6$F*F-F2F2*(\"#DF2-%$sinG6#F*F2-%$co sGF=F2F2\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ode2G/,(-%%diffG6$ -%\"yG6#%\"tG-%\"$G6$F-\"\"#\"\"\"*&$\"\"&!\"#F2-F(6$F*F-F2F2*&#\"#D\" \"$F2F*F2F2$\"#)*!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ode3G/,(- %%diffG6$-%\"xG6#%\"tG-%\"$G6$F-\"\"#\"\"\"*&$\"\"&!\"#F2-F(6$F*F-F2F2 *&\"#DF2F*F2F2\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 105 "Here I'll plot some solutions to the last ode. You can use this as a model for \+ the plots you have to do. " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "\n x1(t) :=simplify(dsolve(\{ode3, x(0) = 1, D(x)(0) = 0\}, x(t)));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>-%#x1G6#%\"tG/-%\"xGF&,$*&#\"\"\"\"&* **RF.*&-%$expG6#,$*&\"#S!\"\"F'F.F7F.,&*&-%$sinG6#,$*(F6F7F/#F.\"\"#F' F.F.F.F/F?F.*&F/F.-%$cosGF " 0 "" {MPLTEXT 1 0 48 "plot ([rhs(x1(t))], t = -10..10, color = black);" }} {PARA 13 "" 1 "" {GLPLOT2D 381 381 381 {PLOTDATA 2 "6&-%'CURVESG6#7g_m 7$$!#5\"\"!$\"3=7uBw%=0C\"!#<7$$!3DKLe9r]X**F-$\"3#e\"4gG:0/6F-7$$!3Gm m;HU,\"*)*F-$\"3%=r\"ojB6m))!#=7$$!3SK$ekynP')*F-$\"3,1F))*y**R_(F87$$ !3I++vV8_O)*F-$\"3;\\'pNe&QWgF87$$!3Wm;/,\\F4)*F-$\"3`q[h1j&[X%F87$$!3 cKLLe%G?y*F-$\"3XWaYij*\\y#F87$$!3Z+]i:?ya(*F-$\"3]B'o[VPe1\"F87$$!3gm m\"HdNvs*F-$!3m'*z$[C\"=2n!#>7$$!3sK$3-8*G+(*F-$!3_)4niC*[#R#F87$$!3h+ +](oUIn*F-$!3[%=E#\\ChnSF87$$!3vm;zWizX'*F-$!3#)3Q+`98lcF87$$!3)GL$3-) \\&='*F-$!33:F!))=pb:(F87$$!3y+]PfLI\"f*F-$!3%z\"oSR;Z6&)F87$$!3!pmmm \"p0k&*F-$!3)R;DhZ8zq*F87$$!39+vV[Hk;&*F-$!3wO,r3,kM6F-7$$!3PL$3-)*G#p %*F-$!3%zo0m+0ZB\"F-7$$!34\\P4'*>_X%*F-$!3/#=Yu%*o*e7F-7$$!3gm\"z>,:=U *F-$!3V>a2Ohal7F-7$$!35%eky-3\")R*F-$!3te-#\\FlVD\"F-7$$!3#)***\\P/,WP *F-$!3CE%z6A/cA\"F-7$$!31L3_vq)pK*F-$!3T!)R(zays6\"F-7$$!3Hm;H2Jdz#*F- $!36G@ja`$yY*F87$$!3-#3xJ7meD*F-$!3Q$=83JT7T)F87$$!3_*\\i!R\"f@B*F-$!3 ;\"Q&zF[#zB(F87$$!3-[U)*f8F87$$!3f$e9;AiZ5*F-$\"3:hXI>n2?JFW7$$!3hm;aQ75y!*F-$\"3'3C+ZoRi (>F87$$!3k\\(oaDS90*F-$\"3@0q7L=@.OF87$$!3mKeRs#zZ-*F-$\"3(yr!z`T7k^F8 7$$!3o:HK*G=\")**)F-$\"3Al5eFkQJmF87$$!3r)**\\iId9(*)F-$\"31TQ3+e5zzF8 7$$!3s\"3xJK'zW*)F-$\"3Mw7F-7$$!3S+D\"yS\"\\6))F-$\"35GhkhE]U7F-7$$! 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