(Solved): Problem 3. Transfer functions and their time-response [40 pts] Consider the following transfer funct ...

Problem 3. Transfer functions and their time-response [40 pts]
Consider the following transfer functions of the 1st order and 2nd order dynamics:

For each transfer function above,

(a) [10 pts] Find the order of the transfer function (the order of system dynamics).

(b) [10 pts] If the transfer function is of the 1st order then find the time constant (?) and dc-gain
(K). Else, if the transfer function is of the 2nd order then find the damping ratio (?), the
natural frequency (?n), and the dc-gain (K).

(c) [10 pts] For the 2nd order transfer functions, determine if the system is (1) Underdamped, (2)
Critically damped, or (3) Overdamped.

(d) [10 pts] Calculate the step response y(t) by inverting the Laplace transform Y (s) = T(s)U(s),
where U(s) = 1/s is the step input.