# Inverse Laplace

1. Mar 11, 2009

### Kruum

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

This isn't a homework, I'm just trying to recap for a mid-term. Anyways, it's about inverse Laplace transformation and this crap is starting to piss me off! How the heck are you supposed to go from $$\frac{ \frac{-U}{s}}{R+sL+ \frac{1}{sC}}$$ to $$- \frac{2 \sqrt{10}}{ \sqrt{15}}e^{-125t}sin(125 \sqrt{15})$$?

2. Relevant equations

The values are: $$U= \sqrt{10}, R=1, L=4*10^{-3}, C=1*10^{-3}$$

3. The attempt at a solution

My best attempt so far has gotten me to $$\frac{-U}{s^2+s(R/L)+(1/LC)}=\frac{- \sqrt{10}}{125 \sqrt{15}} \frac{125 \sqrt{15}}{(s+125)^2+(125 \sqrt{15})^2}$$. I know this is pretty close but not close enough...

2. Mar 11, 2009

### Kruum

I found it out myself. Instead of $$\frac{-U}{s^2+s(R/L)+(1/LC)}$$ I should have had $$\frac{-U/LC}{s^2+s(R/L)+(1/LC)}$$. This gives me the right answer.

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