1. a) Simplify the block diagram as far as possible.
b) Select values for Kp and tau that will include a second order response that has a damping factor of 0.125 and a natural frequency of 10rad/s.
c) For a step input of magnitude 1.0 find the output as a function of time using numerical methods. Give the results in a table OR graph.
d) For a step input of magnitude 1 find the output as a function of time by integrating the differential equation (i.e., using the homogeneous and particular solutions).
e) Compare the values found in steps c) and d).
f) For the transfer function; 1) apply a phasor transform and express the gain and phase angle as a function of frequency, 2) calculate a set of values and present them in a table, 3) use the values calculated in step 4) to develop a frequency response plot on semi-log paper, 5) draw a straight line approximation of the Bode plot on semi-log paper.