{VERSION 5 0 "IBM INTEL NT" "5.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 45 "Simulation of vibration
 of a stretched string" }{TEXT -1 290 "\n\nSolution is decomposed into
 Fourier components.  Note that each Fourier component (or \"partial w
ave\") oscillates as a standing wave, but when they are superposed wit
h the proper amplitudes and phase relationships, they form a wave puls
e that bounces back and forth.\n\nInstructions for use:" }}{PARA 259 "
" 0 "" {TEXT -1 431 "Start with cursor at the first line of red text i
n the file.  Keep pressing the enter key, waiting for the computer to \+
finish the computation each time.  In order to run the animation, sele
ct the graph, then click on the \"play button\" on the tool bar (looks
 like a triangle pointing to the right).  If you change some function \+
or parameter, you only need to re-run the \"execution groups\" below t
hat point where you made the change." }}{PARA 256 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 
"restart; with(plots); with(plottools);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 88 "f := (n,x,t) -> sin(n*Pi*x)*cos(n*Pi*t);\na := array(
1..5,[0.4244,0.5,0.2546,0,-0.0606]);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 167 "p := [seq(animate(a[j]*f(j,x,t),x=0..1,t=0..5,frames
=100, color=COLOR(RGB, (j mod 5)/5, (j+1 mod 5)/5, (j+2 mod 5)/5)),j=1
..5)]:\ndisplay(p,title=\"Four Partial Waves\");" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 92 "animate(sum(a[j]*f(j,x,t),j=1..5),x=0..1,t=0.
.5,frames=100,color=black,title=\"Fourier Sum\");" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 266 "p := [seq(animate(a[j]*f(j,x,t),x=0..1,t=0.
.5,frames=100, color=COLOR(RGB, (j mod 5)/5, (j+1 mod 5)/5, (j+2 mod 5
)/5)),j=1..5)]:\np1 := [op(p),animate(sum(a[j]*f(j,x,t),j=1..5),x=0..1
,t=0..5,frames=100,color=black)]:\ndisplay(p1,title=\"Partial Waves an
d Fourier Sum\");" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 1" 267 }{VIEWOPTS 
1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }