# Inverse of Laplace Transform

• Apr 10th 2011, 03:48 AM
heatly
Inverse of Laplace Transform
Iam trying to find the inverse of the attached laplace transform,
Dont know how to rearrange the 1st part to get it into a standard form to apply the inverse?

I've tried using partial Fraction but I have the exponential term I dont know what to do with?
The correct ans is on the bottom of the page.
• Apr 10th 2011, 04:18 AM
Prove It
Hint: $\displaystyle \mathcal{L}^{-1}\left[e^{-as}F(s)\right] = f(t-a)H(t-a)$.
• Apr 10th 2011, 04:34 AM
heatly
thanks prove it ,i'll give it another go
• Apr 10th 2011, 06:36 AM
heatly
I can see that e^(-2t) = H(t-2)

but cant see how to get F(s) out of 1/(s^3 + s)

L{f(t)} = F(s)
• Apr 10th 2011, 08:07 AM
topsquark
Quote:

Originally Posted by heatly
but cant see how to get F(s) out of 1/(s^3 + s)

Hint: What is the Laplace transform of 1 - cos(kt)?

-Dan
• Apr 10th 2011, 09:40 AM
Prove It
Quote:

Originally Posted by heatly
I can see that e^(-2t) = H(t-2)

but cant see how to get F(s) out of 1/(s^3 + s)

L{f(t)} = F(s)

Factorise the denominator and use Partial Fractions.
• Apr 10th 2011, 03:52 PM
heatly
Thanks a heap prove it and topsquark.

I finally got it.