Question

Let us assume x (t) = A cos(ωt + φ), what is the s-domain expression?

(a) Y(s)=H(s) A(Scos Ø-ω sinØ)/(S^2-ω^2)

(b) Y(s)=H(s) A(Scos Ø+ω sinØ)/(S^2+ω^2)

(c) Y(s)=H(s) A(Scos Ø-ω sinØ)/(S^2+ω^2)

(d) Y(s)=H(s) A(Scos Ø+ω sinØ)/(S^2-ω^2)

I got this question in an online interview.

The query is from Transfer Function topic in chapter Application of the Laplace Transform in Circuit Analysis of Network Theory

Answer 1

The correct choice is (c) Y(s)=H(s) A(Scos Ø-ω sinØ)/(S^2+ω^2)

Best explanation: We had the equation Y(s) = H(s)X(s) to find the steady state solution of y(t). The s-domain expression for the response for the input is Y(s)=H(s) A(Scos Ø-ω sinØ)/(S^2+ω^2).