Hi, how should I start to solve the following PDE?

$\displaystyle u_{tt} - u_{xx} = sin(x) cos(5x) sin(w t)$ 0<x<pi, t>0

u(0,t)=u(pi, t)=0

u(x,0)=$\displaystyle u_{t}(x,0)$=0.

My aim is actually to find the values for w, for which the solution does not diverge. Is there a way to find it without completeley solving the problem.

Thanks for the help.