- #1

member 428835

## Homework Statement

Solve 2D wave eq. ##u_tt=c^2 \nabla^2u## in a circle of radius ##r=a## subject to $$u(t=0)=0\\

u_t(t=0)=\beta(r,\theta)\\u_r(r=a)=0\\$$and then symmetry for ##u_\theta(\theta=\pi)=u_\theta(\theta=-\pi)## and ##u(\theta=\pi)u(\theta=-\pi)##.

## Homework Equations

Lot's I'm sure.

## The Attempt at a Solution

So I find a solution for ##u## after applying the above boundary conditions where I have two double sums and two constants to solve for. To solve for these, I use the initial conditions. However, ##u(t=0)=0## does not allow me to solve for either of the two constants since ##u(t=0)## vanishes. Thus I have one initial condition yet two constants, one for each double sum. Any ideas?

I was thinking since the boundary was not moving at ##r=a## perhaps there is some energy requirement solvability condition that should be satisfied but I don't know. Any ideas?