Old spec 3.4 example, dominant poles of a third order system (ENGR5001)

Old spec 3.4 example, dominant poles of a third order systemTutorialOld spec ENGR2022:210 min

A stable system has the Transfer Function $G(s) = \frac{4a}{(s^2 + 2s + 4)(s + a)}, \qquad a > 0$

Formulas you may need

Dominant pole(s): the pole(s) closest to the imaginary axis, which decay most slowly (learn this)
Steady state gain: set $s = 0$ (learn this)

(a)
Find the three poles and the steady state gain.
real part of complex poles =
imaginary part of complex poles (+) =
steady state gain =
(b)
Which pole(s) dominate the transient response when $a = 4$ , and when $a = 0.25$ ? Describe the step response in each case.