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Find the inverse Laplace transform of F (s) = 3 s²+1 O 3 cos t O sin(3t) O cos(3t) O 3 sin t

Find the inverse Laplace transform of F (s) = 3 s²+1 O 3 cos t O sin(3t) O cos(3t) O 3 sin t

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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7) Please help on following multiple choice ASAP!

**Problem Statement:** Find the inverse Laplace transform of \( F(s) = \frac{3}{s^2 + 1} \). **Options:** - ○ \( 3 \cos t \) - ○ \( \sin(3t) \) - ○ \( \cos(3t) \) - ○ \( 3 \sin t \) **Explanation:** The problem requires finding the inverse Laplace transform of the given function \( F(s) \). The Laplace transform is a widely used integral transform in mathematics with applications in engineering and physics. It's crucial for solving linear ordinary differential equations and is often used in control systems and signal processing. To solve this, recall that the inverse Laplace transform of \( \frac{1}{s^2 + a^2} \) is \( \frac{1}{a} \sin(at) \). Here, \( a = 1 \), so the inverse transform of \( \frac{1}{s^2 + 1} \) is \( \sin t \). Considering the coefficient 3 in the numerator, the correct inverse Laplace transform is \( 3 \sin t \). **Correct Answer:** - ○ \( 3 \sin t \)
Transcribed Image Text:**Problem Statement:** Find the inverse Laplace transform of \( F(s) = \frac{3}{s^2 + 1} \). **Options:** - ○ \( 3 \cos t \) - ○ \( \sin(3t) \) - ○ \( \cos(3t) \) - ○ \( 3 \sin t \) **Explanation:** The problem requires finding the inverse Laplace transform of the given function \( F(s) \). The Laplace transform is a widely used integral transform in mathematics with applications in engineering and physics. It's crucial for solving linear ordinary differential equations and is often used in control systems and signal processing. To solve this, recall that the inverse Laplace transform of \( \frac{1}{s^2 + a^2} \) is \( \frac{1}{a} \sin(at) \). Here, \( a = 1 \), so the inverse transform of \( \frac{1}{s^2 + 1} \) is \( \sin t \). Considering the coefficient 3 in the numerator, the correct inverse Laplace transform is \( 3 \sin t \). **Correct Answer:** - ○ \( 3 \sin t \)
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