# Math Help - Laplace of cosh (sorry urgent)

1. ## Laplace of cosh (sorry urgent)

Hi all,

Sorry I hate posting urgent questions up here but either way I need some help.

I'm looking for the laplace of $\cosh^2{t}$ but I've got no idea how to go about it, can anyone help out?

Cheers.

2. Originally Posted by Peleus
Hi all,

Sorry I hate posting urgent questions up here but either way I need some help.

I'm looking for the laplace of $\cosh^2{t}$ but I've got no idea how to go about it, can anyone help out?

Cheers.
$cosh=\frac{e^x+e^{-x}}{2}$

3. Is...

$\cosh^{2} t = \frac{1}{2} + \frac{e^{2t} + e^{-2t}}{4}$ (1)

... so that...

$\mathcal{L} \{\cosh^{2} t\} = \frac{1}{2s} + \frac{1}{4(s-2)} + \frac{1}{4(s+2)}$ (2)

Kind regards

$\chi$ $\sigma$