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Consider an LTI system with transfer function H(s) = 1 / [s (s + 4)] If the input to the system is cos(3t) and the steady state output is A sin(3t + α), then the value of A is

1. 1/30
2. 1/15
3. 3/4
4. 4/3

Correct answer: 1/15

Solution

The steady-state output amplitude A for an LTI system can be determined using the magnitude of the transfer function evaluated at the frequency of the input. For the given transfer function H(s), substituting s = j3 gives a magnitude of |H(j3)| = 1/15, which corresponds to the output amplitude.

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