Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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.](https://content.bartleby.com/qna-images/question/1720cd77-2294-45a6-8b70-43447dc02920/eb5b4588-918b-40bf-8be6-35165afe9296/ouudptr_processed.png)
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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