8. Consider the initial-value, boundary-value problem for a string of length L, pinned at the ends, and governed by the wave equation. In class we used characteristics to find D'Alembert's solution. Here, let L = 1, the initial velocity be zero, and the initial dis- placement be F(x)= [4x, for 0 < x < (1-2), for <r<1' 3 Sketch the solution (as carefully as possible - use a ruler) for the following times. I suggest you wait to divide by 1/2 until after sketching how the curves move to the left and right. That way the slopes can match the t = 0 slopes. And you just take the average of the two translated curves. (a) t=0 (b) t = (c) t=