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(hold shift key or use mouse wheel to zoom it).
Canvas is matched to your browser window.
0 < Xo,Yo < 280.
The script makes 2 it iterations with the time steps
Δt = 0.05 per frame. Set it = 1 and γ = 0
after you get a stationary pattern.
Resonances in circular membrane
A CPU based simulation of the
wave equation with time periodic perturbation.
For this membrane wave eigenmodes are
un,ω(r,φ,t) = Jn(ωr)
sin(nφ) sin(ωt),
where Jn are the Bessel functions
(J2,4,6,8 are shown in Fig.1).
From the boundary condition un,ω(r = 1) = 0 it
follows thet ω are zeros of the Bessel functions. Some of them
you can find below.
ω2 = {5.136, 8.417, 11.62, 14.80, 17.96}
ω4 = {7.588, 11.06, 14.37, 17.62, 20.83}
ω6 = {9.936, 13.59, 17.00, 20.32, 23.59}
ω8 = {12.22, 16.04, 19.55, 22.95, 26.27}
ω10 = {14.48, 18.43, 22.05, 25.51, 28.89}
ω12 = {16.70, 20.79, 24.49, 28.03, 31.46} WebGL Demosupdated 7 August 2010
