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## Homework Statement

Wondering if I did this correctly..

Find the laplace transform:

$$z(t)=e^{-6t}sin(\omega_{1}t)+e^{4t}cos(\omega_{2}t)$$ for ##t\geq 0##

## Homework Equations

## The Attempt at a Solution

For the first part, I assume I can do this, but I'm not too sure. This is my main question, am I allowed to do this?

**$$\mathcal{L}(sin(\omega_{1}t))=F(s+6)$$**

Which gives me:

$$\frac{\omega _{1}}{s^{2}+\omega _{1}^{2}}=\frac{\omega _{1}}{(s-4)^{2}+\omega _{1}^{2}}$$

I figure since:

**$$F(s+a)=\int_{0}^{\infty}f(t)e^{-(s+a)t}dt$$**

I can do the above?

Sorry if this question is stupid, I haven't done laplace transforms in a long time.