Determine ¹{F}. F(s) = 4s²-15s+8 s(s-3)(s-4) Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms.
Determine ¹{F}. F(s) = 4s²-15s+8 s(s-3)(s-4) Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms.
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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![**Educational Content on Laplace Transforms**
---
### Problem Statement:
Determine \( \mathcal{L}^{-1} \{ F \} \).
\[ F(s) = \frac{4s^2 - 15s + 8}{s(s - 3)(s - 4)} \]
---
### Resources:
- [Click here to view the table of Laplace transforms.](#)
- [Click here to view the table of properties of Laplace transforms.](#)
---
### Solution:
\[ \mathcal{L}^{-1} \{ F \} = \boxed{} \]
---
This problem involves taking the inverse Laplace transform of a rational function \( F(s) \). The expression consists of a polynomial in the numerator \( 4s^2 - 15s + 8 \) and a product of linear factors \( s(s - 3)(s - 4) \) in the denominator.
To solve it, one would generally:
1. Perform partial fraction decomposition of \( F(s) \).
2. Use the inverse Laplace transform properties and tables to find the corresponding time-domain function \( f(t) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbbba0909-7b4f-4e80-8e24-06dfda2d061e%2F837731d5-8a65-4fcd-bac6-3e7211ebdcad%2Fqpot9ur_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Content on Laplace Transforms**
---
### Problem Statement:
Determine \( \mathcal{L}^{-1} \{ F \} \).
\[ F(s) = \frac{4s^2 - 15s + 8}{s(s - 3)(s - 4)} \]
---
### Resources:
- [Click here to view the table of Laplace transforms.](#)
- [Click here to view the table of properties of Laplace transforms.](#)
---
### Solution:
\[ \mathcal{L}^{-1} \{ F \} = \boxed{} \]
---
This problem involves taking the inverse Laplace transform of a rational function \( F(s) \). The expression consists of a polynomial in the numerator \( 4s^2 - 15s + 8 \) and a product of linear factors \( s(s - 3)(s - 4) \) in the denominator.
To solve it, one would generally:
1. Perform partial fraction decomposition of \( F(s) \).
2. Use the inverse Laplace transform properties and tables to find the corresponding time-domain function \( f(t) \).
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