GATE AG 2009 • Q5 MCQ • 1 Mark

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Laplace transforms and their inverse

Question Statement:

1/(s² − a²) is the Laplace Transform of

Options:

  • (A) sin at
  • (B) t sin at
  • (C) sinh at
  • (D) a⁻¹ sinh at

Official Answer Key:

D

Step-by-Step Solution & Explanation

Standard transform pair: L{sinh(at)} = a/(s²−a²). Therefore L{(1/a) sinh(at)} = (1/a)·a/(s²−a²) = 1/(s²−a²). So the inverse Laplace transform of 1/(s²−a²) is a⁻¹ sinh(at), matching option (D). Option (C), 'sinh at' without the 1/a factor, is the classic distractor obtained by forgetting to divide by a.

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