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Group I lists a set of four transfer functions. Group II gives a list of possible step responses y(t). Match the step responses with the corresponding transfer functions.
Group I
P = 25/(s² + 25)
Q = 36/(s² + 20s + 36)
R = 36/(s² + 12s + 36)
S = 49/(s² + 7s + 49)
Group II
1. [step response plot]
2. [step response plot]
3. [step response plot]
4. [step response plot]
- P-3, Q-1, R-4, S-2
- P-3, Q-2, R-4, S-1
- P-2, Q-1, R-4, S-3
- P-3, Q-4, R-1, S-2
Correct answer: P-3, Q-2, R-4, S-1
Solution
The correct option matches each transfer function with its corresponding step response based on the characteristics of their poles and zeros. Transfer function P has a simple oscillatory response, Q exhibits a damped response, R shows a critically damped response, and S has an overdamped response, aligning perfectly with the given step response plots.
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(Note: K denotes a constant in the options)
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