I either have to solve the wave equation using Green's functions or Fourier transforms. I am given an infinite string which is fixed at $x_0=0$ and at rest for $t<0$. At $t=0$, it receives an instantaneous blow at $x=0$ which imparts an initial velocity $V\delta (x-x_0)$, where V is a constant. Find the position of the string at time t.
Is the initial velocity a Neumann condition? And if so how would I go about solving this as I now have in-homogeneous boundary conditions. Is the wave equation I want to solve homogeneous? I need help picturing how to set this problem up and what the equation is I am actually trying to solve.