Explanation Given: The given function is f ( t ) = 2 t e t 2 cos t 2 . Concept used: If f ( t ) is a piecewise continuous function and of exponential of order t > 0 then Laplace transform of f ( t ) is given as L ( f ( t ) ) = ∫ 0 ∞ e − s t f ( t ) d t . Calculation: Use the definition above to write the Laplace transform of the given function as show below. L ( f ( t ) ) = ∫ 0 ∞ e − s t ( 2 t e t 2 cos t 2 ) d t = [ e − s t sin e t 2

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Question

Chapter 4.1, Problem 51E

To determine

To show: The given function is not of exponential order but possess a Laplace transform.

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Chapter 4.1, Problem 50E

Chapter 4.1, Problem 52E

Chapter 4 Solutions

Advanced Engineering Mathematics

Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

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The given function is not of exponential order but possess a Laplace transform.

Solution Summary: The author explains that the given function is not of exponential order but possess a Laplace transform.

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To show: The given function is not of exponential order but possess a Laplace transform.

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Chapter 4 Solutions