# Need help with inverse laplace transformation

Karmel

## Homework Statement

(s^3+6s^2-18s+13)/(s(s+1)(s^2-4s+13)

## The Attempt at a Solution

I am so lost on this problem. I have tried it several times and just keep confusing myself. I think that I am messing up just setting up the problem. Can someone please help me out? How do I get this into partial fraction and then where do I go from there.

## Answers and Replies

Unco
Hi Karmel,

Assuming you want to take the inverse Laplace transform of F(s) = (s^3+6s^2-18s+13)/(s(s+1)(s^2-4s+13)), the first step is to decompose it into partial fractions, which I'm sure you would have come across before. There are three such partial fractions, of the form A/s, B/(s+1) and (Cs+D)/(s^2-4s+13), with A, B, C and D constants to be determined.

Show us your work so we know where you're getting stuck.

Karmel
I would love to show my work but after I set it up like showed to me above with the partial fraction I don't know what to do. The book I am using is so unclear on partial fractions. What are the steps?

Karmel
so after doing the partial fractions if I am doing it right I get teh final answer to be

1-e^-s+(s+4)(sin(3s)(e2s)/3)

I really hope that is right cause I have tried it a thousand ways and Iam getting no where...

Homework Helper
You can check your answer using this online calculator:

http://wims.unice.fr/wims/wims.cgi?session=COB95DF175.3&+lang=en&+module=tool%2Fanalysis%2Ffourierlaplace.en [Broken]

I don't know if that link would expire over time, but if it does, just head to the main page and look for the online Fourier-Laplace calculator. Apart from that I'm kind of lazy to work it out.

Last edited by a moderator:
friend sultan
(s^2+2s+1)/(s^3+2s^2+4s+2)

friend sultan
(s^2+2s+1)/(s^3)+2(s^2)+4s+2)

friend sultan
(s^2+2s+1)/((s^3)+2(s^2)+4s+2)

zeroone_1343
can anyone help with this
s((s-a)^0.5)