# inverse laplace transform

• Mar 19th 2008, 07:32 AM
johnbarkwith
inverse laplace transform
does anybody know the inverse laplace transform of (5+s)/(s^2 +2s) , to revert to a function of t again....
• Mar 19th 2008, 08:09 AM
Peritus
partial fraction expansion:

$
\frac{{5 + s}}
{{s(s + 2)}} = \frac{5}
{{s(s + 2)}} - \frac{1}
{{s + 2}} = \frac{a}
{s} + \frac{b}
{{s + 2}} + \frac{1}
{{s + 2}}
$

I'll assume that you'll be able to find the constants a and b.

Now all we need to do is look at the transform table (I'll assume that the TF is casual) :

$
\begin{gathered}
L\left( {e^{at} u(t)} \right) = \frac{1}
{{s - a}} \hfill \\
L\left( {u(t)} \right) = \frac{1}
{s} \hfill \\
\end{gathered}
$

...
• Mar 19th 2008, 09:37 AM
johnbarkwith
is that meant to be 5/s(s+2) + 1/s+2
• Mar 29th 2008, 11:41 PM