Find the free-vibration response of a rectangular membrane of sides \(a\) and \(b\) subject to the following initial conditions:

\[\begin{aligned}& w(x, y, 0)=w_{0} \sin \frac{\pi x}{a} \sin \frac{\pi y}{b}, \quad 0 \leq x \leq a, \quad 0 \leq y \leq b \\& \frac{\partial w}{\partial t}(x, y, 0)=0, \quad 0 \leq x \leq a, \quad 0 \leq y \leq b\end{aligned}\]