Computation of the (n,m) first normal modes of vibration of a square membrane given a certain initial position and velocity. The normal modes are orthogonal functions defined for each variable (x, y) independently, using the method of separation of variables, and depend on the boundary conditions held for each variable.

Below is a short animation of the first 100 normal modes of a square membrane with all its borders fixed, with initial position f(x,y) = sin(x) and initial velocity f'(x,y) = cos(x).