Suppose an elastic bar has constant density, , and Young's modulus, E, uniform cross section, and length L. The bar is initially at the rest and lying flat along the interval [0, L]. At the time 0, it is acted on by a force per unit length, acting parallel to the bar at the right end x = L. Use the Laplace transformation to solve this boundary value problem: 2u t 2 = c 2 2u x 2 for 0 < x < L, t > 0 with c 2 = E B.C.: u(0,t) = 0 and E u x (L,t) = K t > 0 I.C.: u(x, 0) = 0 and u t (x, 0) = 0 x > 0