*(a) Assume that u(r, , t) = a(t)(r, ), where (r, ) are the eigenfunctions of the

Problem 8.6.1

1. Assume  where  are the eigenfunctions of the related homogeneous problem. What initial conditions does a(t) satisfy? What differential equation does a(t) satisfy?
2. What are the eigenfunctions?
3. Solve for .

Step by step solution

Step 1 of 4

Let  be the radius of a forced semicircular membrane, and the  be the corresponding displacement that satisfies the partial differential equation given below,

And the boundary conditions are,

The corresponding initial conditions are,