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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "# G.H. George    ENG
I 9420       2008 06 13" }}{PARA 0 "" 0 "" {TEXT -1 18 "#  Example 9.0
2.3." }}{PARA 0 "" 0 "" {TEXT -1 69 "# Animation of a wave on a fixed \+
string satisfying the wave equation " }{XPPEDIT 18 0 "diff(y,`$`(t,2))
 = 5^2*diff(y,`$`(x,2));" "6#/-%%diffG6$%\"yG-%\"$G6$%\"tG\"\"#*&)\"\"
&F,\"\"\"-F%6$F'-F)6$%\"xGF,F0" }}{PARA 0 "" 0 "" {TEXT -1 31 "#  with
 initial displacement   " }{XPPEDIT 18 0 "y(x,0) = x-x^2;" "6#/-%\"yG6
$%\"xG\"\"!,&F'\"\"\"*$)F'\"\"#F*!\"\"" }{TEXT -1 8 "   (0 < " }{TEXT 
256 1 "x" }{TEXT -1 5 " < 1)" }}{PARA 0 "" 0 "" {TEXT -1 26 "#  and in
itial velocity   " }{XPPEDIT 18 0 "diff(y,t)(x,0) = x-x^2;" "6#/--%%di
ffG6$%\"yG%\"tG6$%\"xG\"\"!,&F+\"\"\"*$)F+\"\"#F.!\"\"" }{TEXT -1 8 " \+
  (0 < " }{TEXT 259 1 "x" }{TEXT -1 6 " < 1)." }}{PARA 0 "" 0 "" 
{TEXT -1 30 "# Both ends of the string (at " }{TEXT 257 1 "x" }{TEXT 
-1 10 " = 0 and  " }{TEXT 260 1 "x" }{TEXT -1 30 " = 1 ) are fixed for
 all time." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 111 "v(n,x,t) := 8/((2*n-1)*Pi)^3 * sin((2*n-1)*Pi*x) \n*
 (cos(5*(2*n-1)*Pi*t) + sin(5*(2*n-1)*Pi*t)/(5*(2*n-1)*Pi));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>-%\"vG6%%\"nG%\"xG%\"tG,$*,\"\")\"\"\",&*&
\"\"#F-F'F-F-F-!\"\"!\"$%#PiGF2-%$sinG6#*(F.F-F3F-F(F-F-,&-%$cosG6#,$*
*\"\"&F-F.F-F3F-F)F-F-F-*&#F-F>F-*(-F5F;F-F.F1F3F1F-F-F-F-" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "y(x,t) := sum(v(n,x,t),n=1..10);" }
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