Find f(t). f(t) = L 6s - 1 s²(s + 1)³) {
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 Statement
Find \( f(t) \).
\[
\mathcal{L}^{-1} \left\{ \frac{6s - 1}{s^2 (s + 1)^3} \right\}
\]
### Solution
\( f(t) = \) [Enter the solution here]
---
#### Explanation:
The problem involves finding the inverse Laplace transform \(\mathcal{L}^{-1}\) of the given function in the frequency domain:
- **Numerator:** \(6s - 1\)
- **Denominator:** \(s^2 (s + 1)^3\)
Understanding the properties of inverse Laplace transforms and partial fraction decomposition may be necessary to approach solving this problem. Once the decomposition is done, each term can be transformed back into the time domain to find \(f(t)\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6589b73f-c70a-44b7-9b99-e4dd330855a5%2F40a759e5-b1c6-4308-9d85-7fff3b11a6bb%2F3js5twb_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement
Find \( f(t) \).
\[
\mathcal{L}^{-1} \left\{ \frac{6s - 1}{s^2 (s + 1)^3} \right\}
\]
### Solution
\( f(t) = \) [Enter the solution here]
---
#### Explanation:
The problem involves finding the inverse Laplace transform \(\mathcal{L}^{-1}\) of the given function in the frequency domain:
- **Numerator:** \(6s - 1\)
- **Denominator:** \(s^2 (s + 1)^3\)
Understanding the properties of inverse Laplace transforms and partial fraction decomposition may be necessary to approach solving this problem. Once the decomposition is done, each term can be transformed back into the time domain to find \(f(t)\).
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