3. In lab 4 we consider the equation y' + 2yy' + way = -k8t - T). In this problem we consider this problem analytically. (a) First consider the case we examine in lab, y' + 40y = -k(t T); y(0) = 0, y'(0) = 1. Find the period T of the unforced response and then solve the problem with Laplace transforms to determine the value of k that will result in the solution being identically zero for all t > T. (b) Now consider y" + y + 40y = -ko(t T); y(0) = 0, y(0) = 1. Repeat your analysis from (a) to find a value of k that will result in the solution being identically zero for all t > T. (c) Plot the solutions from (a) and (b) to show they do what you expect. 3. In lab 4 we consider the equation y' + 2yy' + way = -k8t - T). In this problem we consider this problem analytically. (a) First consider the case we examine in lab, y' + 40y = -k(t T); y(0) = 0, y'(0) = 1. Find the period T of the unforced response and then solve the problem with Laplace transforms to determine the value of k that will result in the solution being identically zero for all t > T. (b) Now consider y" + y + 40y = -ko(t T); y(0) = 0, y(0) = 1. Repeat your analysis from (a) to find a value of k that will result in the solution being identically zero for all t > T. (c) Plot the solutions from (a) and (b) to show they do what you expect