I need help with 8 also. 8. Consider a string that has one end fixed, with the other end free to move in the vertical direction. Suppose the string is put into motion by virtue of the free end's being manually moved up and down periodically. An IB VP describing this motion is azu 2 azu at2 ax2 = 0, 0 to, u(x, to) = 0, 0 to, u(l, 1) = esin (2nct), t > to. Take { = 1, c = 522, to = 0, and e = 10-4. (a) Solve the IBVP with w not equal to a natural frequency of the string. Graph the motion of the string with w equal to half the fundamental frequency. (b) Solve the IBVP with w equal to a natural frequency of the string. Show that resonance occurs. Graph the motion of the string with @ equal to the fundamental frequency