## Questions & Answers

EXERCISE 4.17.13: (Chapter 4, Problem 13 in the 8th Edition). For each of the second-order systems that follow, find Ċ, w₁, Ts, %OS. [Section: 4.6] Tp. Tr, and

EXERCISE | 4.17.21: (Chapter 4, Problem 21 in the 8th Edition).

EXERCISE 4.17.29: (Chapter 4, Problem 29 in the 8th Edition). EXERCISE 4.17.54: (Chapter 4, Problem 54 in the 8th Edition). (a) Consider the translational mechanical system shown below. A I-pound force, f(t), is applied at t = 0. If f = 1, find K and M such that the response is characterized by a 4-second settling time and a 1-second peak time. Also, what is the resulting percent overshoot? [Section: 4.6] G

Q 1 Consider a multiple inputs control system described by a block diagram shown in Fig. 2. Find the complete output for the system when both inputs act simultaneously.

Q 2

Q 3 Determine: (i) the peak time (iii) the rise time (ii) the settling time (ii) the maximum overshoot

Problem 3b (10 points): For the two systems with the following characteristic equations, state whether or not the system is stable and why. i) P(s) = s³ - 2s² + s +1

Consider a multiple inputs control system described by a block diagram shown in Fig. 2. Find the complete output for the system when both inputs act simultaneously.

2. By using partial fraction expansion and the inverse Laplace transform, calculate the original functions y(t) for the following s-domain functions.

1. Find the Laplace transforms of the following functions based on the known Laplace transforms of sin (wt) and cos (wt);