# Thread: Need good source for solving Inverse Laplace complex roots

1. ## Need good source for solving Inverse Laplace complex roots

Hi,
I need to convert this to the time domain. I managed to find some examples with complex roots but they were very different.
Can anyone give me some hints or maybe a good source or book that explains these types?

$\displaystyle L = \frac{5s}{2s^2+18}$

2. ## Re: Need good source for solving Inverse Laplace complex roots

Originally Posted by trojsi
Hi,
I need to convert this to the time domain. I managed to find some examples with complex roots but they were very different.
Can anyone give me some hints or maybe a good source or book that explains these types?

$\displaystyle L = \frac{5s}{2s^2+18}$
\displaystyle \displaystyle \begin{align*} \mathcal{L}^{-1}\left\{\frac{5s}{2s^2 + 18}\right\} &= \frac{5}{2}\,\mathcal{L}^{-1}\left\{ \frac{s}{s^2 + 9} \right\} \\ &= \frac{5}{2}\,\mathcal{L}^{-1}\left\{ \frac{s}{s^2 + 3^2} \right\} \end{align*}

You should be able to find this inverse laplace transform in your tables