(Solved): 1) For each of the transfer functions below, plot the poles and zeros on a s-plane. Find the dampin ...

1) For each of the transfer functions below, plot the poles and zeros on a s-plane. Find the damping ratio and state the nature of the response (overdamped, underdamped, etc.). Finally, calculate the response of each system to a unit step input using inverse Laplace transforms. a) \( G(s)=\frac{5}{(s+3)(s+6)} \) b) \( G(s)=\frac{20}{s^{2}+6 s+144} \) c) \( G(s)=\frac{(s+2)}{s^{2}+9} \) d) \( G(s)=\frac{(s+5)}{(s+10)^{2}} \)