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Math Help - final value

  1. #1
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    final value

    find final value of y(t)

    d4/dt4 y(t) + 4 d3/dt3 y(t) + 3 d2/dt2 y(t) + 5 d/dt y(t) + y(t) = r(t)

    y(t) output
    r(t) input

    thanks
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  2. #2
    MHF Contributor chisigma's Avatar
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    The roots of the polynomial s^{4} + 4\cdot s^{3} + 3\cdot s^{2} + 5\cdot s + 1 have all negative real part so that we can apply the 'final value theorem' and obtain...

    \lim_{t \rightarrow \infty} y(t) = \lim_{s \rightarrow 0} s\cdot \int_{0}^{\infty} r(t)\cdot e^{-st}\cdot dt (1)

    Kind regards

    \chi \sigma
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  3. #3
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    more details final value

    I need more details
    full answer
    regards
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  4. #4
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    Quote Originally Posted by islamatef View Post
    I need more details
    full answer
    regards
    No, what you need is to show some effort - what you've done, how you have used the help given in the reply you got, what specifically you still do not understand etc.
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