A string of length $2L$ is fixed at both ends. The displacements on it satisfy the equation ${\partial^2 y\over \partial t^2}=\nu{\partial^2 y\over \partial x^2}$ . Also, $y(x,0)=0$ and for $t<0$, it oscillates in its fundamental mode. At $t=0$, the change in ${\partial y \over \partial t}=c\delta(x-L)$. How do I find $y(x,t)$ for $t>0$?
Thanks.
I know the form of the general solution to the (free) wave equation, I just don't know how to apply boundary conditions. It would be great if someone would kindly elaborate.