Step by step answers the question.

Using Laplace transform or otherwise, solve the solution u(x, t) for the problem of finding the displacement of an elastic string which is driven by an external force and is determined from Uxx + sin xx cos wt = utt, 00 u(0, t) = 0, u(1, t) = 0, t>0 u(x, 0) = 2 sin 3rx , ut (x, 0) = 4 sin nx, 0