Understand Laplace alot better now

[mathrocks]

Ok, I'm starting to understand Laplace a lot 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.

 

[quantumdude]

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.

 

[mathrocks]

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]

yeah, you'll probably need to review the chapter the step functions/laplace.

By the way, ever heard of convolution integrals?