Laplace transform of step function

[chota]

this isn't homework, this is just general knowledge and i can't figure it out.. please help, thx

Find the Laplace transform of the given function:

f(t) = { 0 t<2, (t-2)^2 t>=2

I tried working it out and this is where i get stuck

f(t) = (t-2)^2 * u(t-2)

I am not sure if I got the write function for f(t), but if I did, I am not sure how to go on with solving this.
Any help is appreciated, Thank YOu
Chota

 

[Peeter]

Are you trying to put this into a form that you can look it up in a table? Your statement "I am not sure if I got the right function for f(t)" is confusing since it's already given.

Seems to me that you can do this by direct substutition into the definition of the transform:

$$F(s) = \int_0^\infty e^{-st} f(t) dt$$

put in your f(t), starting your integral at t=2, make a t-2 change of vars, and integrate by parts a couple times.