# Laplace Transforms

1. Nov 8, 2007

### Moneer81

1. The problem statement, all variables and given/known data

What is the laplace transform of e^(-t) cos 2t u(t-1)

2. Relevant equations

definition of Laplace transform: LT of f(t) = integral of f(t)e^-st dt, where limits of integration are from 0 to infinity

3. The attempt at a solution

since I have u(t-1) then do I just change the limits of integration to go from 1 to infinity instead?

then I guess what is the fastest way to evaluate the resulting integral:
integral of e^-(s+1)t cos 2t dt ?

2. Nov 8, 2007

### sprint

my hint is that the step function has a big influence on the limits of integration since the step function is zero to the left side of when the step function is one.

and then...maybe im not sure, you could use a trigonometry identity

3. Nov 8, 2007

### Moneer81

OK so I was right in changing the lower limit of integration from 0 to 1?

As far as the integral goes, for a similar problem in a book I was reading they ended up with an expression that was somehow obtained from the quotient rule of derivatives...

4. Nov 8, 2007

### sprint

u(t-1)

take t - 1 = 0 -----> t = 1

but im not sure if changing the limits of integration forces you to change the "t's" in the function.

ex. cos 2(t-1) and e^-((s+1)(t-1))