These vibrations in the direction of the x-axis are modeled by the wave equation u_tt = c²u_xx, c² = E/ρ. If the rod is fastened at one end, x = 0, and free at the other, x = L, we have u(0, t) = 0 and u_x(L, t) = 0. Show that the motion corresponding to initial displacement u(x, 0) = f(x) and initial velocity zero is