A process that exhibits second$-$order dynamics has the following transfer function:

$G(s)=\frac{60}{18s^2+12s+3}$

a$.$ What are the gain $($unitless$),$ time constant $($minutes$),$ and damping coefficient $($unitless$)$

for this system?

b$.$ Will this system exhibit overdamped, critically damped, or underdamped response?

Why?

c$.$ Assuming a unit step input is made to the process at time $t=0,$ what will be the percent

overshoot of the response function?

d$.$ At what time $($in minutes$)$ will the response reach its first maximum value?