Explanation Given: The function is f ( t ) = e − t sin t . Definition used: If f ( t ) is a piecewise continuous function and of exponential of order t > 0 then Laplace transform of f ( t ) is expressed as L { f ( t ) } = ∫ 0 ∞ e − s t f ( t ) d t . Calculation: Use the above definition to write the Laplace transform of the given function. L { f ( t ) } = ∫ 0 ∞ e − s t ( e − t sin t ) d t = ∫ 0 ∞ e − ( s + 1 ) t sin t d t = [ e − ( s + 1 ) t ( s + 1 ) 2 + 1 { − ( s + 1 ) sin t − cos t } ] </

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 4.1, Problem 15E

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To find: The expression for the Laplace transform of the given function.

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Chapter 4.1, Problem 14E

Chapter 4.1, Problem 16E

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Chapter 4 Solutions

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The expression for the Laplace transform of the given function.

Solution Summary: The author explains the expression for the Laplace transform of f(t).

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To find: The expression for the Laplace transform of the given function.

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Chapter 4 Solutions