TIME RESPONSE

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

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

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

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

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

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

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)?

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

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

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

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

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

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

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

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

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

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

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?

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

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

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

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?

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

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?

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?

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)?

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

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:

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?

Pole-zero cancellation is considered a valid approximation when:

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

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

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

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?

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?

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

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?

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

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?

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

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

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?

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

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

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

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

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?

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

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

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