# How to solve this forced wave equation?

1. Nov 1, 2011

### c299792458

1. The problem statement, all variables and given/known data
If a system satisfies the equation $\nu^2 {\partial^2 \psi\over \partial x^2}={\partial^2 \psi\over \partial t^2}+a{\partial \psi\over \partial t}-b\sin\left({\pi x \over L}\right)\cos\left({\pi \nu t\over L}\right)$
subjected to conditions: $\psi(0,t)=\psi(L,t)={\partial \psi(x,0)\over \partial t}=0$ and $\psi(x,0)=c\sin\left({\pi x\over L}\right)$,

how might I solve this?
Thanks.

2. Relevant equations

As above.

3. The attempt at a solution

I can solve the equation $\nu^2 {\partial^2 \psi\over \partial x^2}={\partial^2 \psi\over \partial t^2}+a{\partial \psi\over \partial t}$ by separation of variables. But I don't know how to deal with the $b\sin\left({\pi x \over L}\right)\cos\left({\pi \nu t\over L}\right)$ term. Also, what is the "forced component" of $\psi(x,t)$?

2. Nov 1, 2011

### susskind_leon

Laplace transform?

3. Nov 1, 2011

### SteamKing

Staff Emeritus
You might try a trial function of the form Phi (x,t) = K sin (pi x/L) cos (pi nu t/L)

From your post, I am not sure which constant terms nu, a, b, c, or L are known