Laplace of cosh (sorry urgent)

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 $$\displaystyle \cosh^2{t}$$ but I've got no idea how to go about it, can anyone help out?

Cheers.

dwsmith

MHF Hall of Honor
Hi all,

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

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

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

chisigma

MHF Hall of Honor
Is...

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

... so that...

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

Kind regards

$$\displaystyle \chi$$ $$\displaystyle \sigma$$