Use the appropriate algebra and Table of Laplace's Transform to find the given inverse Laplace transform. L^{-1}left{frac{1}{(s-1)^2}-frac{120}{(s+3)^6}right}

Use the appropriate algebra and Table of Laplace's Transform to find the given inverse Laplace transform. L^{-1}left{frac{1}{(s-1)^2}-frac{120}{(s+3)^6}right}

Question
Laplace transform
asked 2021-03-07
Use the appropriate algebra and Table of Laplace's Transform to find the given inverse Laplace transform. \(L^{-1}\left\{\frac{1}{(s-1)^2}-\frac{120}{(s+3)^6}\right\}\)

Answers (1)

2021-03-08
Step 1 It is given that, \(L^{-1}\left\{\frac{1}{(s-1)^2}-\frac{120}{(s+3)^6}\right\}\) Step 2 Obtain the inverse Laplace transform as follows: \(L^{-1}\left\{\frac{1}{(s-1)^2}-\frac{120}{(s+3)^6}\right\}=L^{-1}\left\{\frac{1}{(s-1)^2}\right\}-L^{-1}\left\{\frac{120}{(s+3)^6}\right\}\)
\(=e^{t}t-e^{-3t}t^5(\text{If } L^{-1}\left\{F(s)\right\}=f(t) \text{ then } L^{-1}\left\{F(s-a)\right\}=e^{at}f(t))\)
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