Question

Match List-I (Time domain function) with List-II (Laplace transform).

• A. A-I, B-II, C-III, D-IV
• B. A-I, B-IV, C-III, D-II
• C. A-IV, B-III, C-I, D-II
• D. A-IV, B-III, C-II, D-I

Hint:

Delay → multiply by $e^{-as}$ in Laplace.

Answer 1

The Correct Option is C

Concept: Standard Laplace transforms:

Step 1: $\sin(\omega t)u(t)$ \[ \frac{\omega}{s^2 + \omega^2} \Rightarrow A \rightarrow IV \]

Step 2: Delayed sine \[ \sin\omega(t-a)u(t-a) \rightarrow e^{-as}\frac{\omega}{s^2+\omega^2} \Rightarrow B \rightarrow III \]

Step 3: Exponential sine \[ e^{-at}\sin\omega t \rightarrow \frac{\omega}{(s+a)^2+\omega^2} \Rightarrow C \rightarrow I \]

Step 4: Delayed exponential sine \[ \Rightarrow D \rightarrow II \] \[ \therefore \text{Correct answer is (C)} \]