# Inverse Laplace Transforms

1. Jun 1, 2014

### Spoolx

1. The problem statement, all variables and given/known data
f(s) = -5s/S^2+9

2. Relevant equations
I think
f(t) cosωt = f(s) s/s^2+ω^2

3. The attempt at a solution
ω=3

-5cos(3t)

Can anyone tell me if I did this correctly? I think I did but just want to make sure, if not can you tell me what I did wrong?

Thanks

2. Jun 1, 2014

### CAF123

There is not really much of a problem statement there but, going by the title, I think you are after the inverse laplace transform of $f(s) = -5 \frac{s}{s^2+9}$. Yes, your result is correct. $$\mathcal{L}^{-1} f(s) \equiv Y(t) = -5 \cdot \mathcal{L}^{-1}\left( \frac{s}{s^2+9}\right) = -5 \cos 3 t$$

3. Jun 1, 2014

### Spoolx

I just wanted to verify my answers, I dont have asolutions manual and want to make sure I am doing the problems correctly.

Thank you

4. Jun 1, 2014

### Ray Vickson

$$f(s) = -\frac{5s}{s^2}+9$$
but it would be correct if you had written
$$f(s) = -\frac{5s}{s^2+9}$$
In text you would write this using parentheses: f(s) = -5s/(s^2+9). Such a simple step to avoid confusion!

5. Jun 1, 2014

### Spoolx

I am sorry, the way you wrote it the second way is the way it was supposed to be written.. guess I need to learn to make proper equations.

Thanks again