Explanation Given: The given expression is L − 1 { s + π s 2 + π 2 e − s } . Formula used: If the Laplace transform of L − 1 { F ( s ) } = f ( t ) and a > 0 , then the second translation property of the inverse Laplace transform is expressed as follows, L − 1 { e − a s F ( s ) } = f ( t − a ) U ( t − a ) The formulae for the inverse Laplace transform are as follow, L − 1 { s s 2 + k 2 } = cos k t L − 1 { k s 2 + k 2 } = sin k t Calculation: Compare the given expression with the L − 1 { e − a s F ( s ) } then, F ( s ) = s + π s 2 + π 2 and a = 1 Rearranging the F ( s ) as follows, F ( s ) = s + π s 2 + π 2 = s s 2 + π 2 + π s 2 + π 2 Use the theorem above to write the inverse Laplace transform of the given function

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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The blank in the statement “ L − 1 { s + π s 2 + π 2 e − s } = _ _ _ _ _ _ ”.

Solution Summary: The author compares the given expression with the formulae for the inverse Laplace transform.

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To fill: The blank in the statement “L−1{s+πs2+π2e−s}=______”.

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Chapter 4 Solutions