Math Help - Laplace of Heaviside function

1. (SOLVED) Laplace of Heaviside function

I need to find the laplace transform of
$(1-\pi)u_\pi-(t-\pi)u_{2\pi}$

I can see how to find the first part of it with the formula

$L[u_c(t)f(t-c)]=e^{-cs}F(s)$

But the second part $(t-\pi)u_{2\pi}$ doesn't seem to work with that. How do I start to solve the second part?

2. Originally Posted by Carbon
I need to find the laplace transform of
$(1-\pi)u_\pi-(t-\pi)u_{2\pi}$

I can see how to find the first part of it with the formula

$L[u_c(t)f(t-c)]=e^{-cs}F(s)$

But the second part $(t-\pi)u_{2\pi}$ doesn't seem to work with that. How do I start to solve the second part?
This is really common with Laplace transform's. You need to use some algebra to fix the problem.

$(t-\pi)u_{2\pi}=(t-\pi-\pi +\pi)u_{2\pi}=(t-2\pi)u_{2\pi}+(\pi)u_{2\pi}$

Now you can apply the theorem to both terms.