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Math Help - La place inverse

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    La place inverse

    F(s) = s+1/(s^2 + 2s + 10)^2 Find the La place inverse transform
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    Quote Originally Posted by mahm32 View Post
    F(s) = s+1/(s^2 + 2s + 10)^2 Find the La place inverse transform
    You have F(s) = \frac{s + 1}{([s + 1]^2 + 3^2)^2} = G(s + 1) where G(s) = \frac{s}{(s^2 + 3^2)^2}.

    From a well known theorem: LT^{-1}[G(s + 1) = e^t g(t) where g(t) = LT^{-1}[G(s)].

    To get g(t), first note that G(s) = \frac{dK}{ds} where K(s) = - \frac{1}{2} \left(\frac{1}{s^2 + 3^2} \right).

    Now use the well known theorem that LT^{-1}\left[\frac{dK}{ds}\right] = - t k(t) where k(t) = LT^{-1}[K(s)].
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    Thanks a lot .
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