Find the inverse of Laplace transform frac{2s+3}{(s-7)^4}

BolkowN 2020-12-30 Answered
Find the inverse of Laplace transform
2s+3(s7)4
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Expert Answer

Roosevelt Houghton
Answered 2020-12-31 Author has 106 answers

Step 1
Find
L1{2s+3(s7)4}
For this take partial fraction
2s+3(s7)4=2(s7)3+17(s7)4
Step 2
Use linearity property of Inverse Laplace transformation
That is , for function f(s),g(s) and a,b be any constants.
L1{af(s)+bf(s)}=aL1{f(s)}+bL1{g(s)}
Step 3
Now equation (i) becomes
L1{2s+3(s7)4}=L1{2(s7)3}+L1{17(s7)4}=e7tt2+17e7tt36
Formula used
L1(F(s))=f(t)
L1(F(Sa))=eatf(t)
L1(n!Sn+1)=tn

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