Question

The inverse Laplace transform of F(s) = \frac{5}{s^2-9} is ______________ (a) \frac{1}{6}e^{3t} + \frac{5}{6e^{-3t}} (b) \frac{1}{6}e^{3t} – \frac{5}{6e^{-3t}} (c) \frac{5}{6}e^{3t} + \frac{5}{6e^{-3t}} (d) \frac{5}{6}e^{3t} – \frac{5}{6e^{-3t}} This question was addressed to me in an international level competition. This intriguing question comes from Problems on Initial and Final Value Theorem topic in division 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) \frac{5}{6}e^{3t} – \frac{5}{6e^{-3t}} To explain I would say: F (t) = L^-1{F(s)} = L^-1{\frac{5}{s^2-9}} = L^-1{\frac{A}{s-3} + \frac{B}{s+3}} Hence, A = (s-3) \frac{5}{(s-3)(s+3)}|_{s=3} = \frac{5}{6} And, B = (s+3) \frac{5}{(s-3)(s+3)}|_{s=-3} = -\frac{5}{6} The inverse Laplace transform is \frac{5}{6}e^{3t} – \frac{5}{6e^{-3t}}.