Explanation Given: The function is e t sin 3 t . Theorem used: First translation theorem, states that if L { f ( t ) } = F ( s ) and a is any real number, then L { e a t f ( t ) } = F ( s − a ) , where L { f ( t ) } denotes the Laplace transform of the function f ( t ) . Calculation: The function is given as follows: e t sin 3 t Here f ( t ) = sin 3 t Use the result L { sin k t } = k s 2 + k 2 and substitute k = 3 . L { sin 3 t } = 3 s 2 + 3 2 = 3 s 2 + 9 Use the first translation theorem, L { e a t f ( t ) } = L { f ( t ) } | s → s − a

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 4.3, Problem 7E

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The Laplace transform of the function etsin3t.

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Chapter 4.3, Problem 6E

Chapter 4.3, Problem 8E

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The Laplace transform of the function e t sin 3 t .

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