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Let us assume x (t) = A cos(ωt + φ), What is the final steady state solution for y (t)?

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Let us assume x (t) = A cos(ωt + φ), What is the final steady state solution for y (t)?

(a) A|H(jω)|cos⁡[ωt+Ø+ θ (ω)]

(b) A|H(jω)|cos⁡[ωt-Ø+ θ (ω)]

(c) A|H(jω)|cos⁡[ωt-Ø- θ (ω)]

(d) A|H(jω)|cos⁡[ωt+Ø- θ (ω)]

I have been asked this question in quiz.

This interesting question is from Transfer Function in section Application of the Laplace Transform in Circuit Analysis of Network Theory

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Correct choice is (a) A|H(jω)|cos⁡[ωt+Ø+ θ (ω)]

The explanation: We obtain the steady state solution for y (t) by taking the inverse transform of Y(s) ignoring the terms generated by the poles of H (s). Thus yss(t) = A|H(jω)|cos⁡[ωt+Ø+ θ (ω)] which indicates how to use the transfer function to find the steady state response of a circuit.

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