How Do You Approach Solving a Forced Wave Equation with Sinusoidal Terms?

[c299792458]

Homework Statement

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.

Homework Equations

As above.

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)?

 

[susskind_leon]

Laplace transform?

 

[SteamKing]

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