Allied & ICAR Exam Bank • ALLIED_2716 NAT • 2 Marks

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Laplace transforms and their inverse

Question Statement:

The inverse Laplace transform $\mathcal{L}^{-1}\left\{\frac{s}{s^2 + 16}\right\}$ is $\cos(k t)$. The integer $k$ is:

Answer Key:

4

Step-by-Step Solution & Explanation

Since $\omega^2 = 16 \implies \omega = 4$, $\mathcal{L}^{-1}\left\{\frac{s}{s^2 + 4^2}\right\} = \cos(4t)$. Thus $k = 4$.
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