Understanding Laplace Transform of f(t)

[georgeh]

i have f(t) defined piece-wise and continous..
f(t) = 0, t < 2pi
t-pi , pi <=t<2pi
0 , t >=2pi

i have so far g(t)=U_pi*f(t-pi)-U_2pi*f(t-pi)
if i do the laplace,
i get e^-pis/s^2-e^-2pis/s^2
in the book, they have
e^-pi*s/s^2 -e^-2pi*s/s^2 (1+pi*s)
I am not sure how they got the factor of (1+pi*s)
..

 

[FrogPad]

Are you sure f(t) is correct. You have:
f(t) = \left\{ \begin{array}{l} 0, \,\, t&lt;2\pi \\ t-\pi, \,\, \pi \leq t &lt; 2\pi \\ 0, \,\, t \geq 2\piSo when t&lt;2\pi and \pi \leq t &lt; 2\pi \\ it equals 0 and t-\pi. I'm assuming you mean f(t) = 0|t&lt;\pi ?

I got (assuming f(t) is wrong):

\frac{e^{-\pi s}}{s^2} - \frac{\pi e^{-2\pi s}}{s} - \frac{e^{-2\pi s}}{s^2}

 

[georgeh]

sorry, what i meant was
on the first interval, t < pi, not two pi.