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Math Help - Laplace/Inverse Laplace Questions

  1. #1
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    Laplace/Inverse Laplace Questions

    I have to find Laplace transform of:

    \frac{1}{4}t^7e^\frac{-1t}{2}

    Here is what I have:

    \frac{1}{4}\frac{7!}{s^8}\frac{1}{s+\frac{1}{2}}

    which simplifies to:

    \frac{1260}{s^8(s+\frac{1}{2})}

    Is this ok??



    Also, I have to find inverse Laplace of:


    \frac{-8}{(s-7)^5}

    Do I need to use partial fractions on this, or is there a simpler way?

    Thanks
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  2. #2
    A Plied Mathematician
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    I think you're not using the LT theorems correctly. Perhaps you're inverting the order of application? I get 1260/(s+1/2)^8.

    For your inverse LT, I would use the shifting theorem first, and then the nth power theorem.
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  3. #3
    MHF Contributor chisigma's Avatar
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    For both questions I soggest You to remember one of the basic properties of the Laplace Tranform...

    \displaystyle \mathcal{L} \{f(t)\} = F(s) \rightarrow \mathcal{L}\{f(t) \ e^{a t}\} = F(s-a) (1)

    Kind regards

    \chi \sigma
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