SOLVED: Laplace Transforms for Step Functions.

[Ricemarine]

I'm savoring my posts before I reach lifer ...

Anyhow, I have the step function equation
f(t) =
{ 0 , t < pi
{ t - pi , pi <= t < 2pi
{ 0 , t >= 2pi

So I tried plugging it in
L{ (t-pi)Upi - (t-pi)U2pi }

= e^-piS L(t) - e^-2piS L(t + pi) <--- I think I went wrong there...

the answer should be (e^-piS / S^2) - ( e^-2piS / S^2)(1+piS)

What I'm confused about is that the c's for f(t-c)Uc do not match for the second part, so I'm wondering what is the right way of doing it. So if anyone can help, thanks.

Edit
To prevent bumping this thread up, I'll update the OP. I got the answer finally (with help from a friend in a different class, awesome ). Our DE teacher never told us it had a name, we just have a table of these things.

Anyhow,
it should be
(t - pi)Upi - (t - 2pi + pi)Up2
= e^-piS / S^2 - e^-2piS L{t-2} - pi *e^-2pi

which becomes the answer above

Thanks for helping Fenixgoon and hypn0tik!

 

[Fenixgoon]

oh man i haven't done la place transforms in two years. me two years ago would be able to solve this in a heartbeat

as i recall, the transform for a step function is 1/s

and according to a table on wiki, u(t-x) = exp(-x*s)/s


oh, and if your function's value is f(t) = t - pi for t >= pi and t < 2pi... you have a ramp, not a step


edit: sorry, my post hasn't been helpful at all. i'm trying to re-learn this so i can help you

the first part of the answer is a delayed ramp function. the delay comes in the form of the exponential, and the ramp is 1/s^2

the second part is delayed by 2pi, but i'm still trying to figure out where the (1+piS) comes from

 

[hypn0tik]

Look at your function f(t). In the interval [pi, 2pi], you DON'T have a step function since f(t) = t -pi. The value of f(t) changes in that interval linearly, so you have a ramp instead.

http://en.wikipedia.org/wiki/L...ted_Laplace_transforms

Take a look at that table and try to work it out using a ramp instead of a step. Scroll up for a table that include the properties such as time shifting.