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Math Help - characteristic equation and stability

  1. #1
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    characteristic equation and stability

    Determine whether each of the following characteristic equations represent a stable or unstable system.

    a/ s3 + 6s2 + 11s + 6 = 0

    b/ s3 + s2 - 8s - 12 = 0

    any ideas guys??

    Thanks
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by conners84 View Post
    Determine whether each of the following characteristic equations represent a stable or unstable system.

    a/ s^3 + 6s^2 + 11s + 6 = 0

    b/ s^3 + s^2 - 8s - 12 = 0

    any ideas guys??

    Thanks
    The question is asking is these cubics have one or more of roots with real part greater than 0.

    For the first s=-1 is an obvious root, so you can factorise and use the quadratic formula to find the remaining roots.

    For the second Descartes rule of signs tell you that the cubic has exactly one positive root.

    CB
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