How do I find the Laplace Transform for U3(t)(t-3)^5/2?

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Discussion Overview

The discussion revolves around finding the Laplace Transform of the function ${U}_{3}(t){(t-3)}^{5/2}$. Participants explore the application of Laplace transforms, particularly in the context of functions involving the unit step function.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty in starting the problem involving the Laplace transform of ${U}_{3}(t){(t-3)}^{5/2}$.
  • Another participant references a formula for Laplace transforms involving the unit step function, suggesting that it may be applicable to the problem at hand.
  • A participant acknowledges the reference but indicates that they did not find a corresponding form in their table of Laplace transforms.
  • One participant admits to struggling with the problem but later claims to have resolved their confusion.

Areas of Agreement / Disagreement

The discussion does not reach a consensus on the approach to solving the problem, as participants express varying levels of understanding and success.

ineedhelpnow
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I'm working on a few problems to find Laplace transforms and I got stuck on this one.
${U}_{3}(t){(t-3)}^{5/2}$

It looks different from the other I've been doing so I don't really know how to get started
 
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According to a table I have, if we are given:

$$f(t)=g(t)u(t-a)$$ where $0\le a$

then:

$$F(s)=e^{-as}\mathcal{L}\{g(t+a)\}(s)$$

Does this help?
 
thank you :) i didn't notice anything of that form in my table
 
So I tried to work on this problem but I can't seem to figure it out. I just have no idea what I'm doing with it.
 
nervmind! got it
 

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