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Inverse Laplace transform

  1. Feb 13, 2014 #1

    I would like to find the inverse Laplace transform for


    I have tried to expand it using the following partial fraction decomp to find the constants and take the inverse Laplace but this did not work

    C1(s)+ C2/(s^2+16) + C3(s)+C4/(s^2+16)^2

    Does anyone have any suggestions?
  2. jcsd
  3. Feb 14, 2014 #2


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    Homework Helper

    First try to find
    $$\mathcal{L}^{-1} \left\{ \frac{1}{(s^2+16)} \right\}$$
    Then use the integration rule
    $$\mathcal{L}^{-1} \{ \mathrm{F}(s) \} = t \, \mathcal{L}^{-1} \left\{ \int_s^\infty \! \mathrm{F}(u) \, \mathrm{d}u \right\}
    \text{or the convolution rule}
    \mathcal{L}^{-1} \left\{ G(s)H(s) \right\} = \int_0^t g(t-\tau)h(\tau) \mathop{d\tau}
    \mathcal{L}^{-1} \{ \mathrm{G}(s) \} =g(t)
    \mathcal{L}^{-1} \{ \mathrm{H}(s) \} =h(t)

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