| M | A | T | H |
| 2 | 1 | B |
Evolution of a membrane. We assume the amplitude u(x,y,t) satisfies the wave type equation
utt = uxx + uyy - uxxxx = T(u) .If the initial condition is an eigenvector u(x,y,0) = bn m sin(n x) sin(m y)to the operator T then u(x,y,t) = bn m sin(n x) sin(m y) cos(cnm t)where cnm is the square root of n2+m2+n4 (which is the negative of the eigenvalue of T). In general (as in the simulation to the right), the initial condition is a linear combination of eigenfunctions. The evolution is the sum of the evolutions of the eigenfunctions. |
Wave simulation with Mathematica. 2000 frames were computed. The background music is from "Lambada" by Kaoma. |