Question

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

(a) |H(jω)|e^j[θ (ω)+Ø]

(b) A/2|H(jω)|e^j[θ (ω)+Ø]

(c) |H(jω)|e^-j[θ (ω)+Ø]

(d) A/2 |H(jω)|e^-j[θ (ω)+Ø]

The question was posed to me by my college professor while I was bunking the class.

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

Answer 1

Right answer is (b) A/2|H(jω)|e^j[θ (ω)+Ø]

Explanation: The expression of k1 becomes K1 = A/2|H(jω)|e^j[θ (ω)+Ø]. We obtain the steady state solution for y(t) by taking the inverse transform ignoring the terms generated by the poles of H(s).