Find the inverse Laplace transform of (1)/((s^2+1)(s^2−2s+7))

Leonard Dyer

Leonard Dyer

Answered question

2022-11-22

Find Inverse Laplace Transform of 1 ( s 2 + 1 ) ( s 2 2 s + 7 ) .

Answer & Explanation

ysik92ASw

ysik92ASw

Beginner2022-11-23Added 13 answers

Hint. By a partial fraction decomposition, one may avoid convolution, getting
20 ( s 2 + 1 ) ( s 2 2 s + 7 ) = s + 3 ( s 2 + 1 ) s + 1 ( s 2 2 s + 7 )
then, by using the Inverse Laplace Transform, we have
L 1 ( s + 3 ( s 2 + 1 ) ) ( t ) = 3 sin ( t ) + cos ( t ) ,
L 1 ( s + 1 ( s 1 ) 2 + 6 ) ( t ) = e t 6 ( 2 sin ( 6 t ) + 6 cos ( 6 t ) ) .

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