# Understand Laplace alot better now

Ok, I'm starting to understand Laplace alot better now. But I have, hopefully, my last question. If you have a function like

g(t)=t^2 * sin(3t) * x(t) where x(t) has an already defined laplace transform.

do you actually include x(t) in your laplace transformation? Because when I see other problems that have u(t) at the end you don't really do anything with them, you only worry about the terms in front of it. Like f(t)=sin(3t)u(t), the answer is simply 3 / (s^2 + 9)....u(t) is not included in it.

Tom Mattson
Staff Emeritus
Gold Member
mathrocks said:
g(t)=t^2 * sin(3t) * x(t) where x(t) has an already defined laplace transform.

do you actually include x(t) in your laplace transformation?
Yes, you do.

Because when I see other problems that have u(t) at the end you don't really do anything with them, you only worry about the terms in front of it. Like f(t)=sin(3t)u(t), the answer is simply 3 / (s^2 + 9)....u(t) is not included in it.
That's because u(t)=1 over the entire range of integration in the transform. If you had instead u(t-a), a>0, then you could not just drop it.

Tom Mattson said:
That's because u(t)=1 over the entire range of integration in the transform. If you had instead u(t-a), a>0, then you could not just drop it.

So for the problem:
g(t)=t^2 * sin(3t) * x(t)

How would you go about transforming that? This is my first encounter of 3 terms...

GCT