Please provide steps The inverse Laplace transform for F(s)=8/(s+9)-6/(s^2-sqrt3)

Albarellak 2020-10-25 Answered

Please provide steps
The inverse Laplace transform for
F(s)=8s+96s23 is
a) 8e9t6sinh(3t)
b) 8e9t6cosh(3t)
c) 8e9t6sinh(3t)
d) 8e9t6cosh(3t)

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Expert Answer

liingliing8
Answered 2020-10-26 Author has 95 answers
Step 1
Consider the function:
F(s)=8x+96x23
Find Inverse Laplace Transform.
Apply Partial fraction on 6x23
6x23=Ax34+Bx+34
6=A(x+34)+B(x34)
Let x=34  and  x=34 and find A and B
A=334
B=334
F(s)=8x+9334(x34)+334(x+34)
Step 2
Inverse Laplace transform property
L1{af(s)+g(s)}=aL1{f(s)}+L1{g(s)}  and  L11s+a=eat
L1{8x+9334(x34)+334(x+34)}=8L1{1x+9}334L1{1x34}+334L1{1x+34}
=8e9t334e34t+334e34t
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