Find the inverse Laplace transform of: (2s)/((s+1)^2+4)

Baqling 2022-09-11 Answered
Find the inverse Laplace transform of: 2 s ( s + 1 ) 2 + 4
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Answers (1)

allelog5
Answered 2022-09-12 Author has 19 answers
Hint:
Note that
L 1 ( 2 s ( s + 1 ) 2 + 4 ) = 2 L 1 ( s + 1 ( s + 1 ) 2 + 4 1 ( s + 1 ) 2 + 4 ) .
Using linearity, it is thus enough to find the inverse Laplace Transform of s + 1 ( s + 1 ) 2 + 4 and of 1 ( s + 1 ) 2 + 4 . To find these, use standard inverse Laplace transforms along with the fact that
L 1 ( F ( s a ) ) = e a t f ( t ) ,
where F is the Laplace transform of f (with a = 1 in your problem).

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