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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 139 "Oscillations of a circu
lar membrane\n(from Mathematical Methods in the Physical Sciences, 3rd
 Ed., Mary Boas, p. 644)\n\nInstructions for use:" }}{PARA 257 "" 0 "
" {TEXT -1 546 "The full animations are not stored in this file in ord
er to save space.  In order to view, you must increase the \"frames\" \+
parameter to around 60 and re-run the calculation.  On a fast PC compu
ter, it may still take a few minutes to compute the last one.  To run \+
the calculation, you should place the cursor on the first block of red
 text and hit \"Enter\".  Keep hitting \"Enter\" to cycle through the \+
\"execution blocks\" (i.e. red text).  Once the animations are ready, \+
you can click on one to select it, then click on the play button on th
e toolbar." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 106 "restart; with(plots); with(plottools);\naddcoords(z_
cylindrical,[z,r,theta],[r*cos(theta),r*sin(theta),z]):" }}{PARA 7 "" 
1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n
" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7W%(animateG%*animate3dG%-animatec
urveG%&arrowG%-changecoordsG%,complexplotG%.complexplot3dG%*conformalG
%,conformal3dG%,contourplotG%.contourplot3dG%*coordplotG%,coordplot3dG
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plot3dG%)gradplotG%+gradplot3dG%-implicitplotG%/implicitplot3dG%(inequ
alG%-listcontplotG%/listcontplot3dG%0listdensityplotG%)listplotG%+list
plot3dG%+loglogplotG%(logplotG%+matrixplotG%(odeplotG%'paretoG%*pointp
lotG%,pointplot3dG%*polarplotG%,polygonplotG%.polygonplot3dG%4polyhedr
a_supportedG%.polyhedraplotG%'replotG%*rootlocusG%,semilogplotG%+setop
tionsG%-setoptions3dG%+spacecurveG%1sparsematrixplotG%+sphereplotG%)su
rfdataG%)textplotG%+textplot3dG%)tubeplotG" }}{PARA 7 "" 1 "" {TEXT 
-1 43 "Warning, the name arrow has been redefined\n" }}{PARA 12 "" 1 "
" {XPPMATH 20 "6#7F%$arcG%&arrowG%'circleG%%coneG%'cuboidG%&curveG%&cu
tinG%'cutoutG%)cylinderG%%diskG%-dodecahedronG%(ellipseG%,ellipticArcG
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torusG%*transformG%*translateG%%vrmlG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 224 "k := (n,m) -> BesselJZeros(n,m);\nf := (n,m,r,theta,
t) -> BesselJ(n,k(n,m)*r)*cos(n*theta)*sin(k(n,m)*t);\ndf := (n,m,r,th
eta,t) -> k(n,m)*BesselJ(n,k(n,m)*r)*cos(n*theta)*cos(k(n,m)*t);\na :=
 (n,m) -> -1.0*df(n,m,0.0,0.0,0.0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%\"kG%-BesselJZerosG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6'%
\"nG%\"mG%\"rG%&thetaG%\"tG6\"6$%)operatorG%&arrowGF,*(-%(BesselJG6$9$
*&-%\"kG6$F49%\"\"\"9&F:F:-%$cosG6#*&F4F:9'F:F:-%$sinG6#*&F6F:9(F:F:F,
F,F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#dfGf*6'%\"nG%\"mG%\"rG%&the
taG%\"tG6\"6$%)operatorG%&arrowGF,**-%\"kG6$9$9%\"\"\"-%(BesselJG6$F4*
&F1F69&F6F6-%$cosG6#*&F4F69'F6F6-F=6#*&F1F69(F6F6F,F,F," }}{PARA 11 "
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-%#dfG6'9$9%$\"\"!F4F3F3$!#5!\"\"F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 152 "plot3d(sum(sum(a(n,m)*df(n,m,r,theta,0.0),m=1..5),n=
0..4),r=0..1,theta=0..2*Pi,coords=z_cylindrical,grid=[20,40],title=\"I
nitial Velocity Distribution\");" }}{PARA 13 "" 1 "" {GLPLOT3D 400 
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 236 "a := (n,m) -> -1.0*df(n,m,0
.5,0.0,0.0);\nanimate3d(sum(sum(exp(-0.2*k(n,m)*t)*a(n,m)*f(n,m,r,thet
a,t),m=1..5),n=0..5),r=0..1,theta=0..2*Pi,t=0..2.5,coords=z_cylindrica
l,frames=2,grid=[30,60],title=\"Drum Struck Off-Center; With Damping\"
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