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{SECT 0 {PARA 18 "" 0 "" {TEXT 256 15 "Homework 5.4 #8" }}{SECT 0 
{PARA 3 "" 0 "" {TEXT -1 16 "Define constants" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 45 "m1 := 3;\nm2 := 2;\nl1 := 5;\nl2 := 5;\ng := 9.8
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#m1G\"\"$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#m2G\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#l1G\"
\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#l2G\"\"&" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"gG$\"#)*!\"\"" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT 
-1 16 "Define equations" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "o
de1 := \n(m1+m2)*l1^2*diff(theta1(t),t$2)+\nm2*l1*l2*diff(theta2(t),t$
2)+\n(m1+m2)*l1*g*theta1(t)=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%o
de1G/,(-%%diffG6$-%'theta1G6#%\"tG-%\"$G6$F-\"\"#\"$D\"*&\"#]\"\"\"-F(
6$-%'theta2GF,F.F5F5*&$\"%]C!\"\"F5F*F5F5\"\"!" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 87 "ode2 := m2*l2^2*diff(theta2(t),t$2)+\nm2*l1*l2
*diff(theta1(t),t$2)+\nm2*l2*g*theta2(t)=0;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%%ode2G/,(-%%diffG6$-%'theta2G6#%\"tG-%\"$G6$F-\"\"#\"
#]*&F2\"\"\"-F(6$-%'theta1GF,F.F4F4*&$\"$!)*!\"\"F4F*F4F4\"\"!" }}}}
{SECT 0 {PARA 3 "" 0 "" {TEXT -1 26 "Solve for general solution" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "dsolve(\{ode1,ode2\},\{theta
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\"tG,$*&-%%sqrtG6#\"#5\"\"\",**&%$_C1GF/-%$expG6#,$*&-F,6#,&!#:F/*&\"
\"$F/F+F/!\"\"F/F(F/#\"\"(\"#:F/F>*&%$_C2GF/-F46#,$F7#!\"(FAF/F>*&%$_C
3GF/-F46#,$*&-F,6#,&F;F/*&F=F/F+F/F/F/F(F/F?F/F/*&%$_C4GF/-F46#,$FNFGF
/F/F/#F/\"\"#/-%'theta1GF',*F1F/FBF/FIF/FSF/" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<$/-
%'theta1G6#%\"tG,**&%$_C1G\"\"\"-%$expG6#*&^#$\"+p8E4B!\"*F,F(F,F,F,*&
%$_C2GF,-F.6#*&^#$!+p8E4BF4F,F(F,F,F,*&%$_C3GF,-F.6#*&^#$\"+'fRd4\"F4F
,F(F,F,F,*&%$_C4GF,-F.6#*&^#$!+'fRd4\"F4F,F(F,F,F,/-%'theta2GF',*F*$!+
I)Q6e\"F4*($\"+I)Q6e\"F4F,F6F,F7F,!\"\"*($\"+I)Q6e\"F4F,F>F,F?F,F,*(FX
F,FFF,FGF,F," }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 24 "Setup initial c
onditions" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "ics := \ntheta1
(0)=pi/6,\ntheta2(0)=0,\nD(theta1)(0)=0,\nD(theta2)(0)=0;" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%$icsG6&/-%'theta1G6#\"\"!,$%#piG#\"\"\"\"\"'/
-%'theta2GF)F*/--%\"DG6#F(F)F*/--F66#F2F)F*" }}}}{SECT 0 {PARA 3 "" 0 
"" {TEXT -1 18 "Solve and simplify" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 46 "dsolve(\{ode1,ode2,ics\},\{theta1(t),theta2(t)\});" }
}{PARA 12 "" 1 "" {XPPMATH 20 "6#<$/-%'theta2G6#%\"tG,$*&-%%sqrtG6#\"#
5\"\"\",**&%#piGF/-%$expG6#,$*&-F,6#,&!#:F/*&\"\"$F/F+F/!\"\"F/F(F/#\"
\"(\"#:F/#F>\"#C*&#F/FCF/*&F2F/-F46#,$F7#!\"(FAF/F/F>*(#F/FCF/F2F/-F46
#,$*&-F,6#,&F;F/*&F=F/F+F/F/F/F(F/F?F/F/*(FMF/F2F/-F46#,$FQFJF/F/F/#F/
\"\"#/-%'theta1GF',*F1FM*(FMF/F2F/FGF/F/*(FMF/F2F/FNF/F/*(FMF/F2F/FWF/
F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 12 
"" 1 "" {XPPMATH 20 "6#<$/-%'theta2G6#%\"tG,**&%#piG\"\"\"-%$expG6#*&^
#$\"+p8E4B!\"*F,F(F,F,$!+g%y!)e'!#6*($\"+g%y!)e'F7F,F+F,-F.6#*&^#$!+p8
E4BF4F,F(F,F,!\"\"*($\"+g%y!)e'F7F,F+F,-F.6#*&^#$\"+'fRd4\"F4F,F(F,F,F
,*(FCF,F+F,-F.6#*&^#$!+'fRd4\"F4F,F(F,F,F,/-%'theta1GF',*F*$\"+nmmmTF7
*(FVF,F+F,F;F,F,*(FVF,F+F,FEF,F,*(FVF,F+F,FLF,F," }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}{PARA 12 "" 1 "" {XPPMATH 20 
"6#<$/-%'theta2G6#%\"tG,&*&%#piG\"\"\"-%$cosG6#,$F($\"+'fRd4\"!\"*F,$
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{MPLTEXT 1 0 9 "evalf(%);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<$/-%'the
ta2G6#%\"tG,&*&%#piG\"\"\"-%$cosG6#,$F($\"+'fRd4\"!\"*F,$\"+#p:wJ\"!#5
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