Show the characteristic roots indicated in Problem 2.163 (a)-(d) in the \(s\)-plane and describe the nature of the response of the system in each case.

Data From Problem 2.163:-

The characteristic roots of a single-degree-of-freedom system are given below. Find all the applicable features of the system among the characteristic equation, time constant, undamped natural frequency, damped frequency, and damping ratio.

a. \(s_{1,2}=-4 \pm 5 i\)

b. \(s_{1,2}=4 \pm 5 i\)

c. \(s_{1,2}=-4,-5\)

d. \(s_{1,2}=-4,-4\)