# BASIC LAPLACE - Unit Step.

1. Apr 18, 2010

### meb09JW

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

Find the Laplace transform of cos(t)h(t)
if the LT of h(t) (unit step) is 1/s

2. Relevant equations

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3. The attempt at a solution

Since the unit step isn't shifting anything anywhere, can I just treat it as 1? Seems too simple, haha. Any ideas? thanks.

2. Apr 19, 2010

### meb09JW

Here's a similar one - Find the LT of (e^-3t + 2)h(t)
with h(t) the same as before.

Would the h(t) just act as a 'turn on' in these cases?

3. Apr 19, 2010

### vela

Staff Emeritus
Yes, and as you noted, it's superfluous with the usual Laplace transform. If you are using the double-sided transform, the presence of the step function would effectively give you the one-sided transform.

4. Apr 19, 2010

### meb09JW

Ok, thanks.

So would the above LT simply be-

1/(s+3) + 2/s

?

5. Apr 19, 2010

### vela

Staff Emeritus
Yup.

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