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Help with finding roots for transfer functions

  1. Oct 5, 2005 #1


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    I am in a Systems and Vibrations class but am currently doing differential equations.

    A problem I am doing requires me to find the transfer function [X(s)/F(s)] and compute the characteristic roots.

    So far I have:

    X(s)/F(s) = (6s +4)/(s^2+14s+58)

    That is the transfer function but now i have to find the roots.

    I realize I only concern myself with the s^2+14s+58 part and set it equal to 0.

    I can't factor it because of obvious reasons. I tried the quadratic equation but my calculator says its a non-real result which means its complex.

    My problem is that I cant figure out how to do the quadratic when there is a complex root.

    I know as^2 + bs + c = a[(s + sigma)^2 + omega^2] = 0.

    However, I cant figure out how to find the roots using this equation.

    Cany anyone help me with this?


  2. jcsd
  3. Oct 5, 2005 #2


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    Homework Helper

    Do you mean that you just want to find the complex roots of the quadratic,

    s² + 14s + 58 = 0 ?

    Can't you just use the quadratic formula ?
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