What is the Laplace Transform of cos(3t)*u(t)?

[JonForbes]

Homework Statement

I need to know what the laplace transform is for f(t) * u(t)

More specifically, h(t) = cos(3t)*u(t)

Homework Equations

I know that f(t-t_o) * u(t-t_o) = e^-t_os * F(s)

The Attempt at a Solution

So, f(t) = cos(3t)

F(s) = s/(s² + 9)

In the formula I gave in (2), I would then think that t_o = 0, because we just are multiplying f(t) by u(t - 0).

So H(s) = e^-0*s * F(s)

H(S) = 1* F(s) = s/(s² + 9)

I think this is right but could someone confirm this?

Thanks!

 

[HeisenBerg46]

H(s)=*L(cos(3t)(s))=s/(s^2+9)
because L(cos(omega*t)(s)=s/(s^2+omega^2) for real s and s/(s^2+a) for complex s