Find the inverse Laplace Transform of s-7 s²+2s+5 2e-t cos(2t) + e-t sin(2t) 4e-t cos(2t) – e-t sin(2t) O 4e -t O et cos(2t) + 2e-¹ sin(2t) O 2e-t cos(2t) - e-t sin(2t) O et cos (2t) - 4e-* sin(2t)
Find the inverse Laplace Transform of s-7 s²+2s+5 2e-t cos(2t) + e-t sin(2t) 4e-t cos(2t) – e-t sin(2t) O 4e -t O et cos(2t) + 2e-¹ sin(2t) O 2e-t cos(2t) - e-t sin(2t) O et cos (2t) - 4e-* sin(2t)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.4: Multiple-angle Formulas
Problem 41E
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![**Problem Statement:**
Find the inverse Laplace Transform of
\[
\frac{s-7}{s^2+2s+5}
\]
**Answer Choices:**
1. \( 2e^{-t} \cos(2t) + e^{-t} \sin(2t) \)
2. \( 4e^{-t} \cos(2t) - e^{-t} \sin(2t) \)
3. \( e^{-t} \cos(2t) + 2e^{-t} \sin(2t) \)
4. \( 2e^{-t} \cos(2t) - e^{-t} \sin(2t) \)
5. \( e^{-t} \cos(2t) - 4e^{-t} \sin(2t) \)
**Description:**
This problem asks you to determine the inverse Laplace transform of a given rational expression. The expression provided is typically associated with second-order linear differential equations. Each answer choice represents a potential time-domain function. The goal is to apply Laplace transform techniques and match the correct inverse to one of the provided solutions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4fb02365-efda-4f71-9185-5332218a7cc4%2Ffbd36e83-a44d-465f-b2ca-d409e4356f2a%2F7f86uo5_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the inverse Laplace Transform of
\[
\frac{s-7}{s^2+2s+5}
\]
**Answer Choices:**
1. \( 2e^{-t} \cos(2t) + e^{-t} \sin(2t) \)
2. \( 4e^{-t} \cos(2t) - e^{-t} \sin(2t) \)
3. \( e^{-t} \cos(2t) + 2e^{-t} \sin(2t) \)
4. \( 2e^{-t} \cos(2t) - e^{-t} \sin(2t) \)
5. \( e^{-t} \cos(2t) - 4e^{-t} \sin(2t) \)
**Description:**
This problem asks you to determine the inverse Laplace transform of a given rational expression. The expression provided is typically associated with second-order linear differential equations. Each answer choice represents a potential time-domain function. The goal is to apply Laplace transform techniques and match the correct inverse to one of the provided solutions.
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