Using the equation of motion given in Problem 8.59, find the natural frequencies of a circular membrane of radius \(R\) clamped around the boundary at \(r=R\).

Data From Problem 8.59:-

Starting from fundamentals, show that the equation for the lateral vibration of a circular membrane is given by \[\frac{\partial^{2} w}{\partial r^{2}}+\frac{1}{r} \frac{\partial w}{\partial r}+\frac{1}{r^{2}} \frac{\partial^{2} w}{\partial \theta^{2}}=\frac{ho}{P} \frac{\partial^{2} w}{\partial t^{2}}\]