Allied & ICAR Exam Bank • ALLIED_2720 NAT • 1 Mark

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Laplace transforms and their inverse

Question Statement:

The Laplace transform of $f(t) = e^{-3t} \sin(2t)$ is $\frac{2}{(s + a)^2 + b^2}$. The value of $a$ is:

Answer Key:

3

Step-by-Step Solution & Explanation

By first shifting theorem, $s$ is replaced by $s - (-3) = s + 3$. Thus $a = 3$ (and $b = 2$).
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