Explanation Given: The given function is e − 2 t cos 4 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 − 2 t cos 4 t Here f ( t ) = cos 4 t Use the result L { cos k t } = s s 2 + k 2 and substitute k = 4 . L { cos 4 t } = s s 2 + 4 2 = s s 2 + 16 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 8E

To determine

The Laplace transform of the function e−2tcos4t.

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Chapter 4.3, Problem 7E

Chapter 4.3, Problem 9E

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The Laplace transform of the function e − 2 t cos 4 t .

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