Question Bank • QB_EM_DE_010 NAT • 2 Marks

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Laplace transforms and their inverse

Question Statement:

The inverse Laplace transform of $F(s) = \frac{s}{s^2 + 16}$ is $f(t) = \cos(\omega t)$. The value of the angular frequency $\omega$ is ________ (answer in integer).

Answer Key:

4

Step-by-Step Solution & Explanation

From the standard table of Laplace transforms: $\mathcal{L}\{\cos(\omega t)\} = \frac{s}{s^2 + \omega^2}$ Comparing with $F(s) = \frac{s}{s^2 + 16}$: $\omega^2 = 16 \implies \omega = 4$ Therefore, the value of $\omega$ is $4$.
← Previous (QB_EM_DE_011) Next (QB_EM_ADV_063) →

Practice In Authentic CBT Exam Interface

Test your skills under authentic timed conditions with live scoring and AIR percentile ranking.

Launch CBT Mock Test