1. Sketch the polar plot of the frequency response for the following loop transfer functions:
Gc(s)G(s) = 1 / ((1 + 0.25s)(1 + 3s))
Gc(s)G(s) = 5(s^2 + 1.4s + 1) / (s - 1)^2
Gc(s)G(s) = (s - 8) / (s^2 + 6s + 8)
Gc(s)G(s) = 20(s + 8) / (s(s +2)(s + 2))
2. Sketch the Bode diagram representation of the frequency response for the transfer functions give in problem (1).