Question: Prove the following statements and give an explanation for each in your own words by referring to a sample physical system.
(a) The phase lag for a gain is zero.
(b) The amplitude ratio for a first-order system goes to zero as the frequency goes to infinity.
(c) The amplitude ratio for a second-order system with a damping coefficient of 0.50 is not monotonic with frequency.
(d) The phase angle decreases without limit as the frequency increases for a dead time.
(e) For an integrator, the amplitude ratio becomes very large for low frequencies and becomes very small for large frequencies
(f) The amplitude ratio for a PI controller becomes very large at low frequencies.