Question Bank MCQ • 1 Mark Section 1: Mathematical Physics Fourier and Laplace transforms

QB_PH_009: Fourier and Laplace transforms

Question Statement

If $\mathcal{L}\{f(t)\} = F(s)$, the Laplace transform $\mathcal{L}\{f''(t)\}$ is given by:
(A) s^2 F(s) - s f(0) - f'(0)
(B) s^2 F(s) - f(0) - s f'(0)
(C) s^2 F(s) + s f(0) + f'(0)
(D) \frac{1}{s^2} F(s) - s f(0)
Correct Answer
A
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: Standard formula: $\mathcal{L}\{f''(t)\} = s^2 F(s) - s f(0) - f'(0)$.
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