4. Consider the model of a pendulum that is struck with a hammer with force A at time t = T, where T > 0. This system can be modeled by y" + 2vy' + way = AS(t - T) (a). Suppose we have y = 2 and wo = V8. Find the quasi-period for the unforced oscillator. (b). Now assume the shock occurs when one quasi-period has passed (that is, T is the quasi-period from part (a)). Furthermore, assume that we have the initial condition y(0) = 0, y'(0) = 1. Solve the problem using Laplace transforms and determine the value of A that will result in the solution being identically zero for all t > T. (c). Now assume the shock occurs instead when two quasi-periods have passed (that is, T is twice the quasi-period from part (a)). Again, assume that we have the initial condition y(0) = 0, y'(0) = 1. Repeat your process from part (b) and find the value of A that will result in the solution being identically zero for all t > T. (d). Compare your values of A from parts (b) and (c). Is one larger than the other? Do your results make sense physically