Determine the inverse Laplace transform of the function below. e - 28 (-s+ 18) (s+ 6)(s+ 3)
Determine the inverse Laplace transform of the function below. e - 28 (-s+ 18) (s+ 6)(s+ 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:**
Determine the inverse Laplace transform of the function below.
\[
\frac{ e^{-2s} (-s + 18) }{ (s + 6)(s + 3) }
\]
**Explanation:**
The function is given in the Laplace domain, and the task is to find its inverse Laplace transform. The expression involves:
1. **Exponential Shift**: \( e^{-2s} \) indicates a time delay of 2 units.
2. **Numerator**: \( (-s + 18) \), a linear polynomial.
3. **Denominator**: \( (s + 6)(s + 3) \), which suggests partial fraction decomposition can be used for simplification.
To solve, you will typically apply the properties of the Laplace transform, including time shifting and partial fraction decomposition, to express the function in a form suitable for finding the inverse transform.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F894299d3-9d11-45b0-ba35-3f62b5e6a781%2Fd09c7847-82c6-4127-931e-4d529c46b2f9%2F7zst7i6_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Determine the inverse Laplace transform of the function below.
\[
\frac{ e^{-2s} (-s + 18) }{ (s + 6)(s + 3) }
\]
**Explanation:**
The function is given in the Laplace domain, and the task is to find its inverse Laplace transform. The expression involves:
1. **Exponential Shift**: \( e^{-2s} \) indicates a time delay of 2 units.
2. **Numerator**: \( (-s + 18) \), a linear polynomial.
3. **Denominator**: \( (s + 6)(s + 3) \), which suggests partial fraction decomposition can be used for simplification.
To solve, you will typically apply the properties of the Laplace transform, including time shifting and partial fraction decomposition, to express the function in a form suitable for finding the inverse transform.
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