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Math Help - Manipulating Laplace into form I need...

  1. #1
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    Manipulating Laplace into form I need...

    Hi all,

    I've got something I need to take the laplace of, and it's in the form of

    t^2 H(t-1)

    I know to take advantage of the second shift theorem, I need to rearrange the left hand side so it has (t-1) in the t terms.

    I also know that the final answer is
    (t-1)^2 + 2(t-1) + 1, but I'm unsure of the method to consistently work through and get this solution.

    From memory, it has to do with subbing in (t-1) into the t term, expanding out and doing balancing, but after mucking around for about 30 minutes I can't seem to get it out.

    Can anyone please help with the process? Thank you.

    P.s. Sorry for the non-latex math, I tried with it and am getting some weird errors.
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  2. #2
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    Quote Originally Posted by Peleus View Post
    Hi all,

    I've got something I need to take the laplace of, and it's in the form of

    t^2 H(t-1)

    I know to take advantage of the second shift theorem, I need to rearrange the left hand side so it has (t-1) in the t terms.

    I also know that the final answer is
    (t-1)^2 + 2(t-1) + 1, but I'm unsure of the method to consistently work through and get this solution.

    From memory, it has to do with subbing in (t-1) into the t term, expanding out and doing balancing, but after mucking around for about 30 minutes I can't seem to get it out.

    Can anyone please help with the process? Thank you.

    P.s. Sorry for the non-latex math, I tried with it and am getting some weird errors.
    Note that t^2 = (t - 1)^2 + 2t - 1 = (t - 1)^2 + 2(t - 1) + 2 - 1 = (t - 1)^2 + 2(t - 1) + 1.

    This sort of algebraic re-arrangment is what you have to do (and if you're studying at the level of learning about Laplace transforms then you're meant to be able to this sort of re-arrangement in your sleep).
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  3. #3
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    Firstly, thank's I got the process now.

    Secondly, yes I agree that I should know how to do it, but if I don't I need to learn how to do it. It's completely my fault, but I find math rather difficult. I would give my left arm to have half the understanding of math that you do. But alas, I don't.

    In the mean time however, all I can do is post up my question's that I'm having trouble with and actually try and learn what I'm meant to - and fixing the holes in my knowledge, rather than not trying at all.
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