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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 18 "  VIBRATING STRING" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 150 "Here is \+
a Maple program to animate a vibrating string with initial position gi
ven by a function f defined on the interval from 0 to Pi.  The constan
t " }{XPPEDIT 18 0 "c;" "6#%\"cG" }{TEXT -1 20 " is assumed to be 0." 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 80 "The pro
cedure B calculates the kth coefficient in the Fourier sine series for
 f." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 128 "T
he procedure g calculates the first n terms in the solution of the wav
e equation given for fixed t as Fourier sine series in x." }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 73 " The example here \+
is for the initial position in the shape of a triangle." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "B := " }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 14 "    proc(f,n) " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
39 "       2*int(f(x)*sin(n*x),x=0..Pi)/Pi;" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "    end;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "
 g := " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "   proc(f,n)" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 43 "      sum(B(f,k)*cos(k*t)*sin(k*x),k=1..n);
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end;" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 27 "f := x -> Pi/2-abs(Pi/2-x);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 19 "plot(f(x),x=0..Pi);" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 69 "animate(g(f,50),x=0..Pi,t=0..2*Pi,numpoints=500,fr
ames=50,color=red);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
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