determine the inverse Laplace transform of F. F(s)=frac{e^{-2s}}{(s-3)^3}

banganX 2021-02-24 Answered
determine the inverse Laplace transform of F.
F(s)=e2s(s3)3
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Expert Answer

gotovub
Answered 2021-02-25 Author has 98 answers
Step 1
Let f(t) be the inverse Laplace transform of the given function
F(s)=e2s(s3)3
Take inverse Laplace transform on both sides:
L1[F(s)]=L1[e2s(s3)3]
f(t)=L1[e2s(s3)3]
Use Inverse Laplace Transform Rule :
If L1[F(s)]=f(t), then L1[easF(s)]=H(ta)f(ta) where , H(t) is Heavside step function
Now, we have a = 2 in our case
Hence,
f(t)=H(t2)L1[1(s3)3]
Step 2
Calculation of inverse Laplace Transform of function on right side:
Apply inverse Laplace Transform rule : If L1[F(s)]=f(t), then L1[F(sa)]=eatf(t)
L1[1(s3)3]=e3tL1[1s3]=e3tL1[22s3]
L1[1(s3)3]=e3t12L1[2s3]
L1[1(s3)3]=e3t12t2{ Using L1[n!s(n+1)]=tn}
L1[1(s3)3]=t22e3t
Hence, we get:
f(t)=H(t2)(t22)e3(t2)
Step 3
Answer:
Inverse Laplace Transform is given by:
f(t)=H(t2)(t22)e3(t2)
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