Transforming Cosine with Unit Step?

[meb09JW]

Homework Statement

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

Homework Equations

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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.

 

[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?

 

[vela]

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.

 

[meb09JW]

Ok, thanks.

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

So would the above LT simply be-

1/(s+3) + 2/s

?

 

[vela]

Yup.