BEE FREE BEE Bachelor of Electrical Engineering Signals and Control Systems Questions and Answers 2 — Questions and Answers
Question 1: What is the Laplace transform of a unit ramp function r(t) = t·u(t)?
- 1/s
- 1/s² (Correct answer)
- s
- 1/(s+1)
Correct answer: 1/s²
The Laplace transform of t·u(t) is 1/s².
Question 2: A system with transfer function G(s) = 5/(s² + 4s + 5) has poles at which locations?
- -2 ± j (Correct answer)
- -4 ± j
- -1 ± 2j
- -2 ± 2j
Correct answer: -2 ± j
Using the quadratic formula on s² + 4s + 5 = 0 gives s = -2 ± j1.
Question 3: In a Bode plot, a first-order pole contributes what slope change at its corner frequency?
- -40 dB/decade
- -20 dB/decade (Correct answer)
- +20 dB/decade
- -10 dB/decade
Correct answer: -20 dB/decade
A single real pole introduces a -20 dB/decade asymptotic slope change at the break frequency.
Question 4: What does the Nyquist stability criterion use to determine closed-loop stability?
- Root locus plot
- Bode magnitude only
- Number of encirclements of the -1 point (Correct answer)
- Step response overshoot
Correct answer: Number of encirclements of the -1 point
The Nyquist criterion counts encirclements of the critical point -1+j0 by the open-loop frequency response.
Question 5: For a continuous-time LTI system, if the impulse response h(t) is absolutely integrable, the system is considered:
- Causal
- BIBO stable (Correct answer)
- Marginally stable
- Unstable
Correct answer: BIBO stable
Absolute integrability of the impulse response is the necessary and sufficient condition for BIBO stability.
Question 6: The region of convergence (ROC) of a causal signal's Laplace transform is:
- The entire s-plane
- To the left of the leftmost pole
- To the right of the rightmost pole (Correct answer)
- A vertical strip between two poles
Correct answer: To the right of the rightmost pole
For a right-sided (causal) signal, the ROC extends to the right of the rightmost pole in the s-plane.
BEE FREE BEE Bachelor of Electrical Engineering Signals and Control Systems Questions and Answers 2
What is the Laplace transform of a unit ramp function r(t) = t·u(t)?