{VERSION 3 0 "SGI MIPS UNIX" "3.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "" -1 256 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{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 -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 }3 3 0 -1 -1 -1 0 0 
0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "445/545 Day 11\n" }{TEXT 
256 60 "Undamped harmonic oscillator forced at its natural frequency" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "with(linalg):\nA:=evalm([
[0,1],[-9,0]]);" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 80 "eigenvects(A);\nexpAt:=evalm(exponential(t*A)
);\nexpmAt:=evalm(exponential(-t*A));" }}{PARA 11 "" 1 "" {TEXT -1 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "B:=evalm([[0],[sin(3*t)
]]);\nevalm( expmAt &* B );\nintegral:=map( int , evalm( expmAt &* B )
 , t );" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 70 "X0:=evalm([[x0],[y0]]);\nXt:= evalm( expAt &* X0 + ex
pAt &* integral );" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 61 "Xt:= map(simplify,evalm( expAt &* X0 + ex
pAt &* integral ));\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "pl
ot( subs(x0=1,y0=2,Xt[1,1]), t=0..100, color=black,numpoints=300 );" }
}}}{MARK "3 0 0" 89 }{VIEWOPTS 1 1 0 1 1 1803 }