Question

Let us assume x (t) = A cos(ωt + φ), then the Laplace transform of x (t) is? (a) X(S)=A(Scos Ø-ω sinØ)/(S^2-ω^2) (b) X(S)=A(Scos Ø+ω sinØ)/(S^2+ω^2) (c) X(S)=A(Scos Ø+ω sinØ)/(S^2-ω^2) (d) X(S)=A(Scos Ø-ω sinØ)/(S^2+ω^2) This question was addressed to me in an online quiz. I would like to ask this question from Transfer Function topic in portion Application of the Laplace Transform in Circuit Analysis of Network Theory Select the correct answer from above options network theory questions and answers, network theory questions pdf, network theory question bank, network theory gate questions and answers pdf, mcq on network theory pdf, gate network theory questions and solutions, network theory mcq Test , ies network theory questions, Network theory Questions for GATE EC Exam, Network Theory MCQ (Multiple Choice Questions)

Answer 1

The correct choice is (d) X(S)=A(Scos Ø-ω sinØ)/(S^2+ω^2) Easiest explanation: We use the transfer function to relate the study state response to the excitation source. And we had assumed that x (t) = A cos(ωt + φ). On expanding and taking the laplace transform we get X(s) = AcosØs/(s^2+ω^2)-AsinØs/(s^2+ω^2) = A(Scos Ø-ω sinØ)/(S^2+ω^2).