Determine L^-1[F(s)] for the given F. F(s)=(s-2)/(s^2+2s+3)

melodykap 2021-01-10 Answered

Determine L1[F(s)] for the given F.
F(s)=s2s2+2s+3

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Expert Answer

Malena
Answered 2021-01-11 Author has 83 answers

Step 1
Given information:
F(s)=s2s2+2s+3
Linearity property of inverse Laplace Transform, for function f(s) and g(s) and constants a and b.
L1{af(s)+bg(s)}=aL1{f(s)}+bL1{g(s)}
Step 2
First can be written as,
L1{s2s2+2s+3}=L1{s+1(s+1)2+231(s+1)2+2}
Apply the linearity property and inverse Laplace transform,
L1{s+1(s+1)2+231(s+1)2+2}=L1{s+1(s+1)2+2}3L1{1(s+1)2+2}
=etcos(2t)3et12sin(2t)
=etcos(2t)32etsin(2t)

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