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, finally, calculate the response of each system to a unit step input using inverse laplace transforms. state the nature of each response (overdamped, underdamped, and so on). then calculate the exact response of each system using laplace transform. then find the damping ratio and natural frequency for each second-order system and show that the value of the damping ratio conforms to the type of response (underdamped, overdamped, and so on).
(a) t(s)= {s}/{s+2}
(b) t(s)= {20}/{s^{2}+6s+144}
(c) t(s)= {(s+5)}/{(s+10)^{2}}