3. Find the inverse Laplace transforms of the following funct (a) 6. F(s) = s2 + 4s + 13 (Ь) 5s -85 F(s) = 4. Give your answer as a piecewise-defined step function
3. Find the inverse Laplace transforms of the following funct (a) 6. F(s) = s2 + 4s + 13 (Ь) 5s -85 F(s) = 4. Give your answer as a piecewise-defined step function
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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![**Problem 3: Finding Inverse Laplace Transforms**
The task is to find the inverse Laplace transforms of the following functions and express your answer as a piecewise-defined step function.
**(a)**
\[
F(s) = \frac{6}{s^2 + 4s + 13}
\]
**(b)**
\[
F(s) = 4 \frac{e^{-5s}}{s} - 3 \frac{e^{-8s}}{s}
\]
**Instructions:**
- Use inverse Laplace transformation techniques such as partial fraction decomposition, convolution theorem, or the shifting theorem as needed.
- The goal is to express each solution in a piecewise-defined step function format for clarity in functional behavior over different intervals.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F85346d8e-a543-42db-b008-9fe5a873d3b5%2F7a830305-a46f-4216-a0e7-b99ab5f67611%2Fp4dpu8i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 3: Finding Inverse Laplace Transforms**
The task is to find the inverse Laplace transforms of the following functions and express your answer as a piecewise-defined step function.
**(a)**
\[
F(s) = \frac{6}{s^2 + 4s + 13}
\]
**(b)**
\[
F(s) = 4 \frac{e^{-5s}}{s} - 3 \frac{e^{-8s}}{s}
\]
**Instructions:**
- Use inverse Laplace transformation techniques such as partial fraction decomposition, convolution theorem, or the shifting theorem as needed.
- The goal is to express each solution in a piecewise-defined step function format for clarity in functional behavior over different intervals.
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