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3. In lab 4 we consider the equation y' + 2yy' + wy -kd(t T). In this problem we consider this problem analytically. (a) First consider the case we examine in lab, y" + 40y = -ko(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. 3. In lab 4 we consider the equation y' + 2yy' + wy -kd(t T). In this problem we consider this problem analytically. (a) First consider the case we examine in lab, y" + 40y = -ko(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