$(10$ points$)$ Find the free vibration response of a rectangular clamped membrane of sides a and $b$ subjected to the following initial conditions:

$w(x,y,0)=w_{0}sin(\frac{x}{a}),\frac{\text{d}\text{e}\text{l}\text{w}}{\text{d}\text{e}\text{l}\text{t}}(x,y,0)=w_0^{}$