# What is the natural frequency of a 3rd order system with 3 real roots?

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?

• Natural resonant frequency only really applies, as a concept to 2nd order filters. – Andy aka May 7 '16 at 9:04
• 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 7 '16 at 9:53

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