# Inverse Laplace transformation

1. Mar 29, 2010

### Koshi

1. The problem statement, all variables and given/known data

I'm supposed to find the inverse Laplace transformation of the following equation

2. Relevant equations

G(s) = s+1/s2+25

3. The attempt at a solution

I was thinking of using one of the shifting theorems because I know that L-1 {1/s2+25} is just sin(5t) but I don't know how to get rid of the numerator.

2. Mar 29, 2010

### Staff: Mentor

You should get into the habit of using parentheses to write rational expressions correctly.

This is how what you wrote would be interpreted:
$$G(s) = s + \frac{1}{s^2} + 25$$

Here is what I believe you really meant:
$$G(s) = \frac{s + 1}{s^2 + 25}$$

To convey what I think you meant when you write in on one line, use parentheses.
G(s) = (s + 1)/(s2 + 25)

Split your expression to get G(s) = s/(s2 + 25) + 1/(s2 + 25). From that you can get L-1(G(s)) = L-1( s/(s2 + 25)) + L-1(1/(s2 + 25)), both of which are straightforward.

Last edited: Mar 29, 2010
3. Mar 29, 2010

### Koshi

Yes that is what I meant to type, my mistake.

I didn't even think of separating the numerator of the equation. But I see exactly what you mean.

Thank you so much for the help and the quick reply!