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John_henderson

Express the following in terms of Heavyside Function=> H(t-a) and find its laplace transform Where F(t) = t 0<t<1 0 1<t< 2 1 t>2

  • one year ago
  • one year ago

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  1. John_henderson
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    Hi guys, im new to this topic i would appreciate it if someone can show me in how to proceed forward with this problem.

    • one year ago
  2. TuringTest
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    It's been a while since I've done this, but here's what I'd work from: http://tutorial.math.lamar.edu/Classes/DE/StepFunctions.aspx

    • one year ago
  3. John_henderson
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    Thanks that site looks useful

    • one year ago
  4. John_henderson
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    The examples on the website are kinda difficult to understand, im still kinda confused....?

    • one year ago
  5. TuringTest
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    do you know the \[\mathcal L\{u_c(t)f(t-c)\}=e^{-cs}F(s)\]transform?

    • one year ago
  6. John_henderson
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    Yes i know the forumla but dont know how to apply it yet... Im i suppose to sub in the interval values in first.

    • one year ago
  7. TuringTest
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    For 0<t<1 we have f(t)=t, so let's start with that Now, since for 1<t<2 we have f(t)=0 we need to subtract the t we had at the beginning, and we need to initiate that using the step function with c=1. So, so far that gives us\[f(t)=t-tu_1(t)\]so far so good?

    • one year ago
  8. John_henderson
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    why is f(t)= 0 ? is that from the limits 0<t<1

    • one year ago
  9. TuringTest
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    your step function is\[f(t)=\left\{\begin{matrix}t&&0<t<1\\0&&1<t<2\\1&&t>2\end{matrix}\right.\]correct? if so, then for t between 1 and 2 your function should equal zero

    • one year ago
  10. John_henderson
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    yes thats correct, But why?

    • one year ago
  11. TuringTest
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    you asked why f(t)=0 for 1<t<2... that's why; it's stated in your step function (sorry for the slow replies, my connection is horrible right now) so do you see how\[f(t)=t-tu_1(t)\]satisfies the first two parts of the step function?

    • one year ago
  12. John_henderson
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    Oh right i see, so do i integrate now?

    • one year ago
  13. TuringTest
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    Well first off, I am thinking you want the laplace transforms, not regular integration. We need to do some more manipulation before we can do that. Secondly, we have not yet added the part that will make it such that f(t)=1 for t>2 any ideas how you might do that? (hint: it requires adding a single term, which is another step function)

    • one year ago
  14. John_henderson
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    H(t-a) ?

    • one year ago
  15. TuringTest
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    but the all-important question is"what is a ?".

    • one year ago
  16. John_henderson
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    1 i guess?

    • one year ago
  17. John_henderson
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    well is it?

    • one year ago
  18. John_henderson
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    lol im so confused at the moment, im totally new to this!

    • one year ago
  19. TuringTest
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    no, you need to understand the heavyside function for H(t-1) what is the value when t=2 ?

    • one year ago
  20. John_henderson
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    0

    • one year ago
  21. John_henderson
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    i mean 1 ?

    • one year ago
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