What is the damped frequency of oscillation (omega_d) for a system with poles at s = -3 +/- j4?

Correct answer: 4 rad/s

Explanation

For an underdamped second-order system with complex poles at -sigma_d +/- j*omega_d, the imaginary part, omega_d, directly gives the damped frequency of oscillation, which is the frequency of the decaying sinusoidal component of the time response.

Other questions

Question 1

The output response of a system is the sum of which two responses?

Question 2

What are the values of the Laplace transform variable, s, that cause the transfer function to become infinite?

Question 3

For a first-order system with the transfer function G(s) = a / (s + a), what is the time constant?

Question 4

A system has a transfer function G(s) = 50 / (s + 50). What is the settling time, Ts, for this system?

Question 5

A second-order system response that is characterized by two real poles and a non-oscillatory step response is called what?

Question 6

What is the natural frequency (omega_n) of a second-order system?

Question 7

For a system with the transfer function G(s) = 36 / (s^2 + 4.2s + 36), what are the values of the natural frequency (omega_n) and the damping ratio (zeta)?

Question 8

A damping ratio (zeta) of 1 corresponds to what type of second-order system response?

Question 9

For an underdamped second-order system, what is the definition of Peak Time (Tp)?

Question 10

Given a system with the transfer function G(s) = 100 / (s^2 + 15s + 100), what is its percent overshoot (percent OS)?

Question 11

In the s-plane for an underdamped second-order system, what do vertical lines of constant real part represent?

Question 12

When can a system with more than two poles be approximated as a second-order system?

Question 13

What is a system that initially responds in the opposite direction of its final value known as?

Question 14

How does adding a zero to a two-pole system generally affect the percent overshoot of its step response?

Question 15

In a state-space representation, what are the roots of the equation det(sI - A) = 0 called?

Question 16

What is the state-transition matrix, Phi(t), in the time-domain solution of state equations?

Question 17

The total response of a system solved using the time-domain state equation method is partitioned into which two components?

Question 18

Given a rotational mechanical system with transfer function G(s) = 1/J / (s^2 + (D/J)s + (K/J)), what is the natural frequency, omega_n?

Question 19

What is the rise time, Tr, for a first-order system with the transfer function G(s) = 10 / (s + 10)?

Question 20

A second-order system response has poles at s = -5 +/- j13.23. What is the form of its natural response to a step input?

Question 21

The time for a first-order system's step response to reach 63 percent of its final value is known as the:

Question 22

For an underdamped second-order system with transfer function G(s) = omega_n^2 / (s^2 + 2*zeta*omega_n*s + omega_n^2), the peak time (Tp) is given by which formula?

Question 23

What is the primary factor that determines the percent overshoot (percent OS) of an underdamped second-order system?

Question 24

Consider the system with transfer function T(s) = 24.542 / (s^2 + 4s + 24.542). If a third pole is added at s = -3, how would the step response compare to the original second-order response?

Question 25

Which physical nonlinearity is characterized by a system's inability to respond to small input signals, requiring the input to exceed a certain threshold before an output is produced?

Question 26

What is the correct expression for the Laplace transform of the state vector, X(s), for a system with initial state x(0) and input U(s)?

Question 27

A second-order system with a transfer function G(s) = 900 / (s^2 + 90s + 900) would be characterized as:

Question 28

In the time-domain solution of state equations, the part of the response that depends only on the initial state vector x(0) is called the:

Question 29

For the system in Example 4.7, designed to have a 20 percent overshoot and a settling time of 2 seconds, what is the required value for the inertia, J?

Question 30

Pole-zero cancellation is considered a valid approximation when:

Question 31

What does a pole on the real axis of the s-plane generate in the time response?

Question 33

For a rotational mechanical system, what physical parameters determine the damping ratio (zeta)?

Question 34

A system is defined by the state equations where matrix A has eigenvalues of -2, -3, and -4. What can be concluded about the system's natural response?

Question 35

If a system's step response is experimentally measured and found to be first-order, how can the parameter 'a' of its transfer function G(s) = K / (s + a) be determined?

Question 36

In the s-plane, what do radial lines extending from the origin represent for an underdamped second-order system?

Question 37

A designer wants to achieve a 20 percent overshoot for a second-order rotational system with K=5 N-m/rad. What must the ratio of inertia to stiffness (J/K) be?

Question 38

How does the response of a nonminimum-phase system, such as the one in Figure 4.27, differ from a standard first-order response?

Question 39

If two underdamped systems have poles with the same real part but different imaginary parts, what aspect of their step responses will be virtually the same?

Question 40

A second-order system transfer function is T(s) = 225 / (s^2 + 30s + 225). What is the nature of its response?

Question 41

The response of a system with a zero can be thought of as the sum of what two components?

Question 42

A system is described by the state equation x_dot = A*x + B*u, where the eigenvalues of A are -1, -1, and -5. What is the form of the natural response?

Question 43

What is the primary effect of amplifier saturation on the step response of a motor's angular velocity?

Question 44

What is the peak time (Tp) for a system with the transfer function G(s) = 100 / (s^2 + 15s + 100)?

Question 45

Given a system pole plot, what is the geometric interpretation of the natural frequency, omega_n?

Question 46

A second-order system has a transfer function G(s) = 625 / (s^2 + 625). What is the nature of its step response?

Question 47

For the system with transfer function T(s) = 1/(2s^5 + 3s^4 + 2s^3 + 3s^2 + 2s + 1), what is the settling time (Ts) if it is approximated as a first-order system with pole at s=-1?

Question 48

The eigenvalues of a system's A matrix are -10 and -2. The system is:

Question 49

What is the primary characteristic of the transient response caused by backlash in a gear system?

Question 50

To find the poles of a system represented in state space, one must find the roots of which equation?