5. a. Consider the following wave equation describing the semi-infinite vibrating string problem: J²u მ2 Ox2 u(x, 0) = f(x), x>0 Ju (x, 0) = g(x), x>0 at Ju = (0,t) 0, t>0. дт Find its solution using the method of characteristics. [Assume that u is continuous at x = 0, t = 0.] b. Show that the solution found in part (a) may be obtained by extending the initial position and velocity as even functions (around z = 0). c. Sketch the solution if g(x) = 0 and 1, 4<<5 f(x)= 0, otherwise.