Transforming Cosine with Unit Step?

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Homework Help Overview

The discussion revolves around finding the Laplace transform of functions involving the unit step function, specifically cos(t)h(t) and (e^-3t + 2)h(t). The context is within the subject area of Laplace transforms in calculus.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants explore whether the unit step function can be treated as 1 in the context of Laplace transforms, questioning its necessity in the transformation process. There is also discussion about the role of the unit step function as a 'turn on' for the functions being transformed.

Discussion Status

Participants are engaging with the problem by sharing their thoughts on the relevance of the unit step function in Laplace transforms. Some guidance has been offered regarding the implications of using the unit step function, particularly in relation to one-sided and double-sided transforms.

Contextual Notes

There is a mention of the unit step function not shifting anything, which raises questions about its role in the transformations being discussed. Additionally, the presence of the unit step function in the context of double-sided transforms is noted.

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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.
 
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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?
 
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.
 
Ok, thanks.

meb09JW said:
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

?
 
Yup.
 

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