Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Find the Laplace transform using Laplace tables.
![The image displays a mathematical function, which is expressed as:
\[ f(t) = \sinh^2(3t) \]
This denotes that the function \( f(t) \) is the square of the hyperbolic sine of three times \( t \).
Key points about the hyperbolic sine function:
- The hyperbolic sine function, denoted \( \sinh(x) \), is defined as \( \sinh(x) = \frac{e^x - e^{-x}}{2} \).
- In this function, the expression \( \sinh^2(3t) \) means the square of \( \sinh(3t) \).
There are no graphs or diagrams in the image to explain further.](https://content.bartleby.com/qna-images/question/a9d4f1dd-159d-4044-a522-696d25a3cc6c/ebf1d559-bc9a-4461-87b0-c6a17792ae7b/zxs315r_processed.jpeg)
Transcribed Image Text:The image displays a mathematical function, which is expressed as:
\[ f(t) = \sinh^2(3t) \]
This denotes that the function \( f(t) \) is the square of the hyperbolic sine of three times \( t \).
Key points about the hyperbolic sine function:
- The hyperbolic sine function, denoted \( \sinh(x) \), is defined as \( \sinh(x) = \frac{e^x - e^{-x}}{2} \).
- In this function, the expression \( \sinh^2(3t) \) means the square of \( \sinh(3t) \).
There are no graphs or diagrams in the image to explain further.
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- Use the accompanying tables of Laplace transforms and properties of Laplace transforms to find the Laplace transform of the function below. 6t3e-2t-t5+ cos 2t Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. 26t³e-21-15+ cos 2t} = -arrow_forwardUse the accompanying tables of Laplace transforms and properties of Laplace transforms to find the Laplace transform of the function below. e cos 2t+ e4t-1 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. e-5t cos 2t + e4t -1} =arrow_forward19-24. Use the first translation principle and Table 2.2 (or Table 2.4) to find the inverse Laplace transform.arrow_forward
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