Question

Let us assume x (t) = A cos(ωt + φ), what is the value of k1?

(a) 1/2 H(jω)Ae^jØ

(b) H(jω)Ae^-jØ

(c) H(jω)Ae^jØ

(d) 1/2 H(jω)Ae^-jØ

I have been asked this question in exam.

My question is from Transfer Function topic in portion Application of the Laplace Transform in Circuit Analysis of Network Theory

Answer 1

Right answer is (d) 1/2 H(jω)Ae^-jØ

Explanation: The first two terms on the right hand side of Y(s) determine the steady state response. k1=H(s) (A(scosØ-ωsin⁡Ø))/(s+jω)|s=jω = 1/2 H(jω)Ae^-jØ.