SetDirectory[$HomeDirectory<>"/Documents/handouts/math467/CircularDrum"]

Plucked Circular Drum

soln=16Sin[θ]Sum[BesselJ[1,BesselJZero[1,n]r]Cos[BesselJZero[1,n]t]/(((BesselJZero[1,n])^3)BesselJ[2,BesselJZero[1,n]]),{n,1,10}];

Table[ContourPlot[soln/.{r->Sqrt[(x^2)+(y^2)],θ->ArcTan[x,y]},{x,-1,1},{y,-1,1},PlotLabel->"\!\(\*TemplateBox[<|"boxes" -> FormBox[
RowBox[{
StyleBox["t", "TI"], "=="}], TraditionalForm], "errors" -> {}, "input" -> "t=", "state" -> "Boxes"|>,"TeXAssistantTemplate"]\)"<>ToString[t],Contours->{-0.3,-0.2,-0.1,0.1,0.2,0.3},ContourLabels->Function[{x,y,z},Text[z,{x,y},Background->White]],FrameLabel->{"\!\(\*TemplateBox[<|"boxes" -> FormBox[
StyleBox["x", "TI"], TraditionalForm], "errors" -> {}, "input" -> "x", "state" -> "Boxes"|>,"TeXAssistantTemplate"]\)","\!\(\*TemplateBox[<|"boxes" -> FormBox[
StyleBox["y", "TI"], TraditionalForm], "errors" -> {}, "input" -> "y", "state" -> "Boxes"|>,"TeXAssistantTemplate"]\)"},RegionFunction->Function[{x,y},(x^2)+(y^2)<1]],{t,{0,0.25,0.50,0.75}}]

GraphicsGrid[Partition[%,2,2]]

Export["circdrum.eps",%,"EPS"]

Export["circdrum.pdf",%%,"PDF"]