Allied & ICAR Exam Bank • ALLIED_0078 NAT • 1 Mark

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Laplace transforms and their inverse

Question Statement:

The Laplace transform of the unit step function $u(t - 3)$ is $\frac{e^{-k s}}{s}$. The value of $k$ is:

Answer Key:

3

Step-by-Step Solution & Explanation

By the second shifting theorem, $\mathcal{L}\{u(t - a)\} = \frac{e^{-as}}{s}$. Here $a = 3 \implies k = 3$.
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