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I know the the structure of a 3rd order system is:

\$Q_s=(s+a)(s^2+2\xi\omega ns+\omega n^2)\$

but what do I do if I have something like this?

\$Q_s=(s+4)(s+5)(s+3)\$

How do I measure its natural frequency?

Dean
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gamliel basha
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    Natural resonant frequency only really applies, as a concept to 2nd order filters. – Andy aka May 07 '16 at 09:04
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    Natural frequency is the frequency that a 2nd order term would oscillate at continuously if the damping were zero. So, theoretically, you could combine any two 1st order terms from three, and define a natural frequency. But the $\omega_n$ derived from any one of these combinations would not have any practical implication. – Chu May 07 '16 at 09:53

1 Answers1

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If a system only has real roots the response is comprised of exponential terms and not oscillatory terms. In this case

$$y(t) = C_1e^{-4t} + C_2e^{-5t} + C_3e^{-3t},$$

thus there is no such thing as a natural frequency of this system because there are no oscillating terms in the solution.

JMJ
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