ME or MEng Master of Engineering Control Systems and Dynamics 2

Question 1

For a second-order system to be classified as underdamped, the damping ratio ζ must satisfy:

Accepted Answer

0 < ζ < 1

Answer

An underdamped system has 0 < ζ < 1, producing an oscillatory transient response that decays exponentially to the steady-state value.

Question 2

What is the natural frequency ωn of a simple spring-mass system with mass m and spring constant k?

Accepted Answer

√(k/m)

Answer

From the equation of motion mẍ + kx = 0, the natural frequency is ωn = √(k/m) rad/s.

Question 3

Using the 2% criterion, the settling time Ts of a second-order system is approximately:

Accepted Answer

4/(ζωn)

Answer

The 2% settling time is approximated as Ts ≈ 4/(ζωn), derived from the time constant of the exponential decay envelope.

Question 4

By standard definition, rise time is the time for the step response to travel from:

Accepted Answer

10% to 90% of its final value

Answer

Rise time is conventionally defined as the time for the response to increase from 10% to 90% of its final steady-state value.

Question 5

Critical damping in a mass-spring-damper system occurs when:

Accepted Answer

The damping ratio ζ equals 1

Answer

Critical damping (ζ = 1) gives the fastest return to equilibrium without oscillation, representing the boundary between underdamped and overdamped responses.

ME or MEng Master of Engineering Practice Test

ME or MEng Master of Engineering Practice Test

ME or MEng Master of Engineering Control Systems and Dynamics 2