Find the inverse Laplace transform of frac{6s+15}{(s^2+25)} s>0

illusiia 2020-10-23 Answered
Find the inverse Laplace transform of
6s+15(s2+25)
s>0
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Expert Answer

aprovard
Answered 2020-10-24 Author has 94 answers
Step 1
The given function is
6s+15(s2+25)
s>0
we have to find inverse Laplace Transform of the given function
Step 2
(6s+15)(s2+25)=6s(s2+25)+15(s2+25)
Applying inverse Laplace in both side
L1[(6s+15)(s2+25)]=6L1[6s(s2+25)]+15L1[15(s2+25)]
We know
L1[ss2+a2]=cos(at)
L1[1s2+a2]=1asin(at)
Then
L1[6s+15(s2+25)]=6cos(5t)+155sin(5t)
L1[6s+15(s2+25)]=6cos(5t)+155sin(5t)
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