Allied & ICAR Exam Bank • ALLIED_0082 NAT • 2 Marks

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Laplace transforms and their inverse

Question Statement:

The Laplace transform of $f(t) = \cos(5t)$ is $\frac{s}{s^2 + k}$. The value of $k$ is:

Answer Key:

25

Step-by-Step Solution & Explanation

$\mathcal{L}\{\cos(\omega t)\} = \frac{s}{s^2 + \omega^2}$. Here $\omega = 5 \implies \omega^2 = 25 \implies k = 25$.
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