GATE EE 2022 Set 1 — Question 37
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Control Systems → Time-Domain Analysis → Transient & Steady-State Response
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Question
An LTI system is shown in the figure where The steady state output of the system, to the input , is given as . The values of ‘’ and ‘’ will be
Correct answer
(A) a = 1, b = 10
Solution
For a stable LTI system, each sinusoidal (or DC) component of the input appears at the output scaled by and shifted by . With :With the denominator exactly as printed, : and , so .This gives , , which matches none of the four options. The printed constant term is therefore inconsistent with the choices.The accepted answer corresponds to the denominator (an undamped natural frequency of rad/s, equal to the input frequency):
1.DC component (): , so .
2.At : , so and .
Hence , , which is option (A).Continue learning with Success Tracker
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