1. ## laplace help

f (t) = {1 0 < t < a
{0 a < t < 2a

If f(t + 2a) = f(t), t>0
f(t) is called: _______________

and its graph for 0 < t < 4a looks like:

and

L{f(t)} = ?

2. If You have a function defined as...

$\sigma(t)=\left\{\begin{array}{cc}1,&\mbox{ if }
0a\end{array}\right.$
(1)

... then is...

$\mathcal{L}\{\sigma(t)\} = \frac{1-e^{-as}}{s}$ (2)

Now if $f(t)$ is $\sigma(t)$ 'periodically extended' with period $2a$ is...

$\mathcal{L}\{f(t)\} = \frac{\mathcal{L}\{\sigma(t)\}}{1-e^{-2as}}= \frac{1-e^{-as}}{s\cdot (1-e^{-2as})}$ (3)

Kind regards

$\chi$ $\sigma$