How to solve this forced wave equation?

  • #1

Homework Statement

If a system satisfies the equation [itex]\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)[/itex]
subjected to conditions: [itex]\psi(0,t)=\psi(L,t)={\partial \psi(x,0)\over \partial t}=0[/itex] and [itex]\psi(x,0)=c\sin\left({\pi x\over L}\right)[/itex],

how might I solve this?

Homework Equations

As above.

The Attempt at a Solution

I can solve the equation [itex]\nu^2 {\partial^2 \psi\over \partial x^2}={\partial^2 \psi\over \partial t^2}+a{\partial \psi\over \partial t}[/itex] by separation of variables. But I don't know how to deal with the [itex]b\sin\left({\pi x \over L}\right)\cos\left({\pi \nu t\over L}\right)[/itex] term. Also, what is the "forced component" of [itex]\psi(x,t)[/itex]?
  • #3
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

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