Suppose that the differential equations in Problem 3.27 are models of physical Systems....

Suppose that the differential equations in Problem 3.27 are models of physical Systems.

(a) For each system, give the system modes.

(b) For each system, give the time constants of the system modes.

(c) A unit step u(r) is applied to each system. After how long in time will the system output become approximately constant? How did you arrive at your answer’?

(d) Repeat Paris (a), (b), and (c) for the transfer function of Problem 3.28(b).