# Damping ratio from transfer function

1. Jul 8, 2010

### sgsawant

I have a transfer function for system.

23.23*s + 1.421
------------------------------------- = tf
s^2 + 25.88*s + 1.421

Since the numerator has a non-zero coefficient for "s" I am wary about equating

25.88 = 2 * zeta * omega [the stuff we usually do for calculating the damping ratio].

Can someone shed any light on this?

Regards,

-sgsawant

N.B.: I this question is a copy of the one I asked on the General Forum. I wanted to switch it from General to Classical but couldn't find a way. Please guide if you know.

2. Jul 10, 2010

### Naty1

Can you divide top and bottom on the left side of the equation by 23.23 to get rid of the unwanted coefficient??

3. Jul 10, 2010

### stevenb

I believe that damping ratio is found in the same way. The numerator coefficients set the system zeros, but the denominator coefficients set the poles which control the character of the response (overdamped, underdamped or critically damped).