# 2nd order characteristic equation standart form

1. Dec 6, 2012

### zoom1

A second order system has the following standart form;

http://controls-design.com/mathtex/mathtex.cgi?H%28s%29%3DK%5Cfrac%7B%5Comega_n%5E2%7D%7Bs%5E2%2B2%5Czeta%5Comega_n%20s%2B%5Comega_n%5E2%7D%20%5Cmbox%7B%20for%20%7D%200%20%5Cle%20%5Czeta%20%5Cle%201 [Broken]

However, sometimes the system I confront, doesn't hold that equation. I mean something like
s+1/(s^2 + 5s + 3)

At that point, it looks like the s+1 term on the numerator corresponds to Wn^2
But it shouldn't be if I'm not mistaken.

So, what am I supposed to do in such cases, in order to find the lets say damping ratio ?

Last edited by a moderator: May 6, 2017
2. Dec 7, 2012

### Staff: Mentor

The numerator has nothing to do with the natural frequency exhibited in the denominator. Once you have standardized the expression to have a unity co-efficient for the denominator's s² term, then the other terms of the denominator give you ζ and Ѡn. The numerator can be thought of as K.Ѡn², where K is a gain factor, a constant, and equals whatever it evaluates as.
BTW, I believe you are short of a pair of parentheses in your expression; here, borrow a spare pair of mine: ( )

BTW (2) you didn't get your latex right.http://physicsforums.bernhardtmediall.netdna-cdn.com/images/icons/icon13.gif [Broken]

Last edited by a moderator: May 6, 2017