S + 5 T(s) = K (s + 1)(s2 + 15s +36) (a) What is the value of K in this system so that the steady state error for a unit step input will be 0 (use Bode plots only, no other approach will be accepted!)? (b) Using the K value you found in part (a), determine the steady state output for the sinusoidal input given in the figure below by using BODE plots that you sketch manually. (c) Using the K value you found in part (a), determine the steady state output for the sinusoidal input given in the figure below by using BODE plots obtained from MATLAB. (d) Using the K value you found in part (a), determine the steady state output for the sinusoidal input given in the figure below by calculating the amplitude ratio and phase analytically (without using BODE plots). r(t) 2000 0 1/160 2/160 3/160 time(sec) -2000