Use the Laplace transform table and the linearity of the Laplace transform to determine the following transform. Complete parts a and b below. £{6t³e- e-8t - et cos √/3t} Click the icon to view the Laplace transform table. plz find this and also the limitation of 's'
Use the Laplace transform table and the linearity of the Laplace transform to determine the following transform. Complete parts a and b below. £{6t³e- e-8t - et cos √/3t} Click the icon to view the Laplace transform table. plz find this and also the limitation of 's'
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 Website Transcription:**
---
**Laplace Transform Problem**
Use the Laplace transform table and the linearity of the Laplace transform to determine the following transform. Complete parts a and b below.
\[
\mathcal{L} \{ 6t^3 e^{-8t} - e^{-9t} \cos(\sqrt{3}t) \}
\]
*Click the icon to view the Laplace transform table.*
---
**Part a: Determine the Formula for the Laplace Transform**
\[
\mathcal{L} \{ 6t^3 e^{-8t} - e^{-9t} \cos(\sqrt{3}t) \} = \frac{36}{(s+8)^4} - \frac{s \cos(\sqrt{3})}{(s^2 - 9s + 9)}
\]
(Type an expression using s as the variable.)
---
**Note:**
- The given expression includes terms with exponential and trigonometric components.
- The student is asked to find the Laplace transform and define the limitations of 's'.
- The handwritten note "plz find this and also the limitation of 's'" indicates that, besides finding the transform, determining the domain or regions of convergence for 's' is necessary.
---
This transcription includes a detailed explanation of the task and notes relevant to the educational context.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1720cd77-2294-45a6-8b70-43447dc02920%2Feb5b4588-918b-40bf-8be6-35165afe9296%2Fouudptr_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Website Transcription:**
---
**Laplace Transform Problem**
Use the Laplace transform table and the linearity of the Laplace transform to determine the following transform. Complete parts a and b below.
\[
\mathcal{L} \{ 6t^3 e^{-8t} - e^{-9t} \cos(\sqrt{3}t) \}
\]
*Click the icon to view the Laplace transform table.*
---
**Part a: Determine the Formula for the Laplace Transform**
\[
\mathcal{L} \{ 6t^3 e^{-8t} - e^{-9t} \cos(\sqrt{3}t) \} = \frac{36}{(s+8)^4} - \frac{s \cos(\sqrt{3})}{(s^2 - 9s + 9)}
\]
(Type an expression using s as the variable.)
---
**Note:**
- The given expression includes terms with exponential and trigonometric components.
- The student is asked to find the Laplace transform and define the limitations of 's'.
- The handwritten note "plz find this and also the limitation of 's'" indicates that, besides finding the transform, determining the domain or regions of convergence for 's' is necessary.
---
This transcription includes a detailed explanation of the task and notes relevant to the educational context.
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