Question

Okay how do I find the inverse Laplace? For F(s) = 3/s^4.

Answer 1

we known that the laplace transform t^n is n!/s^(n+1). So since, \[\frac{ 3 }{ s^4 }=\frac{ 3 }{ 3! }*\frac{ 3! }{ s ^{3+1} }=\frac{ 1 }{ 2 }*\frac{ 3! }{ s ^{3+1} }\]
So, the inverse laplace is t^3/2. Do you understand?

Answer 2

why does 3/3! = 3/3! * 3!/s^2+1 ?

Answer 3

oh got it

Answer 4

can't you just look at it and be like 3!/2s^3+1 works?

Answer 5

i dont understand the math :(

Answer 6

Yes you can, I was just going through the steps. But, if you can see that right away, go for it =).
All, I was doing was muliplying the top and bottom by the same term to get the F(s) in a form where I know how to take the inverse laplace.

Answer 7

okay that makes sense but then how do you see t^3/2?

Answer 8

\[F(s) = \frac3{s^4}\]
\[f(t)=\mathcal L\Big\{\frac3{s^4}\Big\}^{-1}\]\[\qquad=\frac 1{2!}\mathcal L\Big\{\frac{3!}{s^4}\Big\}^{-1}\]\[\qquad=\tfrac12t^3\]

Answer 9

because \(3!=3\times2!\)

Answer 10

how did you get 1/2! ?

Answer 11

it's 1/2t^3 !!!!!! not t^3/2 haha but thanks :)