How to find inverse Laplace transform of the following function? X ( s ) =...

hemotropS7A

hemotropS7A

Answered

2022-11-25

How to find inverse Laplace transform of the following function?
X ( s ) = s s 4 + 1
I tried to use the definition: f ( t ) = L 1 { F ( s ) } = 1 2 π i lim T γ i T γ + i T e s t F ( s ) d sor the partial fraction expansion but I have not achieved results.

Answer & Explanation

agyaly1F

agyaly1F

Expert

2022-11-26Added 5 answers

Hint: With
s 4 + 1 = s 4 + 1 + 2 s 2 2 s 2 = ( s 2 + 1 2 s ) ( s 2 + 1 + 2 s )
then
s s 4 + 1 = 2 4 1 s 2 + 1 2 s 2 4 1 s 2 + 1 2 s
then complete the squares in denominators!

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