2. The vibrations along a particular beam u(x, t) with simply supported ends is governed by the following boundary value problem, u(0,t) = (= 22 u(0, t) a.x2 a24 + n a.x4 = 0, at2 un, t) = 0 = u(n,t) ar2 u(x,0) = f(x2) au(a,0) at = g(x) Use the separation of variables method with u(x, t) for the eigenvlaues In. X(x)T(t) to find an expression n = 11