Question

The inverse Laplace transform of F(s) = \frac{2}{s^2+3s+2} is ______________ (a) -2e^-2t + 2e^-t (b) 2e^-2t + 2e^-t (c) -2e^-2t – 2e^-t (d) 2e^-t + e^-2t I have been asked this question in exam. My enquiry is from Problems on Initial and Final Value Theorem topic in chapter 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

Right choice is (a) -2e^-2t + 2e^-t To explain I would say: s^2 + 3s + 2 = (s+2) (s+1) Now, F(s) = \frac{A}{(s+2)} + \frac{B}{(s+1)} Hence, A = (s+2) F(s) |s=-2 = \frac{2}{s+1} |s=-2 = -2 And, B = (s+1) F(s) |s=-1 = \frac{2}{s+2} |s=-1 = 2 ∴ F(s) = \frac{-2}{(s+2)} + \frac{2}{(s+1)} ∴ F (t) = L^-1{F(s)} = -2e^-2t + 2e^-t for t≥0.