Question
Exercise
Consider the wave equation for a vibrating circular membrane inside a disk of radius a
with initial conditions
u(r, 0,0) = 0,
du
(r,0,0) = a(r) sin 0
and fixed boundary conditions
u(a, 0, t) = 0
(a) Solve this problem.
(b) Show that the total energy of the membrane is conserved. What is its value?
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Transcribed Image Text

Exercise Consider the wave equation for a vibrating circular membrane inside a disk of radius a with initial conditions u(r, 0,0) = 0, du (r,0,0) = a(r) sin 0 and fixed boundary conditions u(a, 0, t) = 0 (a) Solve this problem. (b) Show that the total energy of the membrane is conserved. What is its value?

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Initial and Boundary value problem

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