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Math Help - Inverse Laplace Transform

  1. #1
    Member kjchauhan's Avatar
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    Inverse Laplace Transform

    Need help to solve the following:

    Find the inverse Laplace transpose using convolution theorem:

    L^{-1} \left\{ \frac{s}{ \(s^2 + 4\)^3}\right\}

    Thanks.
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  2. #2
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    Re: Inverse Laplace Transform

    Let

    L^{-1} \left\{ \frac{s}{ \(s^2 + 4\)^3}\right\}=L^{-1} \left\{ \frac{s}{ \(s^2 + 4\)}\frac{1}{ \(s^2 + 4\)}\frac{1}{ \(s^2 + 4\)}\right\}=f(t)*g(t)*h(t)

    Then by the convolution theorem we can choose

    L^{-1} \left\{ \frac{s}{ \(s^2 + 4\)}\right\}=f(t)

    L^{-1} \left\{ \frac{1}{ \(s^2 + 4\)}\right\}=g(t)=h(t)

    And you will find these inverse Laplace transforms on Wikipedia.
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