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Math Help - laplace of two function?

  1. #1
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    laplace of two function?

    Hello,
    I need laplace transform of these function:
    f(t)=(t^n)cos(a*t)
    and
    f(t)=(t^n)cosh(a*t)
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  2. #2
    A Plied Mathematician
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    For the first, note that

    \mathcal{L}\left[t^{n}f(t)\right]=(-1)^{n}\dfrac{d^{n}}{ds^{n}}\,F(s),

    and

    \mathcal{L}\left[\cos(at)\right]=\dfrac{s}{s^{2}+a^{2}}.

    For the second, note in addition that

    \mathcal{L}\left[\cosh(at)\right]=\dfrac{s}{s^{2}-a^{2}}.

    Where does that get you?
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  3. #3
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    I want to make laplace transform table to memorize them.
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