Simplifying and Solving Step Functions with Laplace Transform

[EvLer]

ARGH! they drive me crazy! and our TA does not have office hrs this week

what does this thing look like?

f(t) = 10 u(t-1)u(5-t)u(t) ?

and what is the strategy to determine it? actually i need a laplace transform of it, but I need to simplify it first, then maybe i can do it by myself.

Thanks in advance.

 

[AKG]

I'm guessing the u function is 1 when it's argument is greater than or equal to 0, and 0 otherwise? So f(t) is 10 when (t-1) > 0, (5-t) > 0, and t > 0, and f(t) is 0 otherwise.

t > 1
t < 5
t > 0

simplifies to:

t in [1, 5]

So f(t) = 10 when t in [1, 5] and f(t) = 0 otherwise. Of course, if I've got this step function wrong, then you'll have to make appropriate adjustments, but there you go.

 

[EvLer]

Oh, I see... that's a little more understandable. Thanks much! Oh, yeah, sorry forgot to define step, your definition is correct.
Now, since this is a pulse-type waveform, I can represent it as u(t-1) - u(t-5) and the appropriate laplace transform is simple.