Consider the 1D wave equation d^2u/dt^2 = c^2( d^2u/dx^2) with
the following boundary conditions: u(0, t) = ux (L, t) = 0 . (a)
Use separation of variables technique to calculate the eigenvalues,
eigenfunctions and general solution. (b) Now, assume L = π and c =
1. With initial conditions u(x, 0) = 0 and ut(x, 0) = 1, calculate
the solution for u(x, t). (c) With initial conditions u(x, 0) =
sin(x/2) and ut(x, 0) = 2 sin(x/2) −...