The Laplace transform of f(t) is L(f)=1/(s2+2). Find f(t).

GATE 2020 ME (ME1) – Question 13

Engineering Mathematics · Differential Equations: Initial and boundary value problems, Laplace transforms · 1 mark · Multiple choice

The Laplace transform of f(t) is $\mathcal L(f)=1/(s^2+\omega^2)$. Find f(t).

$(1-\cos\omega t)/\omega^2$
$\cos(\omega t)/\omega$
$\sin(\omega t)/\omega$
$(1-\sin\omega t)/\omega^2$

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Correct answer: (C) $\sin(\omega t)/\omega$

Explanation

The standard pair is $\mathcal L\{\sin\omega t\}=\omega/(s^2+\omega^2)$. Divide by ω to obtain the stated numerator 1. Thus **f(t)=sin(ωt)/ω, C**. A cosine would introduce s in the numerator.