(Solved): Solve the problem, Use the general solution of a 2d membrane, but discuss the eigenvalues for values ...

Problem 1: Motion of a square membrane A square membrane with a side length of $L$ is initially distorted into the shape: $\alpha (x,y)=\left(\frac{x}{L}\right)\left(\frac{y}{L}\right)\left(1-\frac{x}{L}\right)\left(1-\frac{y}{L}\right)$ and is then released from rest. Its edges are fixed/clamped for all time. Express the shape of the membrane in terms of the displacement, $u(x,y,t)$.