Minimization of potential energy for a simply supported beam under a uniformly distributed load requires the functional V[u] = [Buz -udx 0 be minimized, where u (x) is the deflection of the beam. The essential boundary conditions for a simply supported beam are u(0) = u(2) = 0. (a) Obtain the exact deflection distribution u (x). (b) Use the Raylegh-Ritz method, with the trial function u(x) = c sin(nx/2) to determine an approximate deflection for the beam. (c) Compare the approximate solution for the deflection at the center of the beam u(1) from (b) with the exact value from (a)