U_{tt} = c^2 \nabla^2 u \text{ for } 0 \le r \le a \text{ and } 0 \le \theta \le 2\pi, \text{ with } t = [0, T]. \text{ The boundary and initial}\text{ conditions will be of the form } u(r, \theta, 0) = f(r, \theta), u_t(r, \theta, 0) = F(r, \theta), u(a, \theta, t) = 0, \text{ for }\text{ all } \theta \text{ on the (circular) boundary.}\text{Let } a = 10 \text{ and } c = 1/2 \text{ with } f(r, \theta) = \left(\frac{100 - r^2}{10}\right) \sin(2\theta) \text{ and } F(r, \theta) = 0, \text{ over a}\text{ suitable time interval } t = [0, \text{up to you}].
