You are given the following simulation diagram, e(t) S a a2 + DET S S a3 y(t) a) Find the transfer function H(s) = y(s)/e(s). b) For a = 0.2, a2 = 1.0 and a3 = 3.0, plot the Bode diagram (that is both the magnitude and phase diagrams). Specifically, calculate by hand the magnitude and phase at input frequency = 1.0 rad/sec, 0.8 rad/sec, 1.2 rad/sec, 2.0 rad/sec etc. c) For an input of e(t) = sin(t), what is the steady state time response of the output. d) For e(t) equal to the unit step, find the solution (equation) for the time response for y(t) (as a function of time only). Illustrate your calculations graphically on the s- plane. Plot y(t) for at least 10 points.