Damping ratio is defined to conveniently divide the underdamped, critically damped, and overdamped conditions at unity for a second-order system.
The damping ratio (zeta) is defined by
where is defined above in Eq.(E.8) as the peak frequency divided by the peak bandwidth, and and are defined above in Eq.(E.7).
As shown in Eq.(E.9), a damping factor of 1 is critically damped, while a damping factor less than 1 is underdamped, and is overdamped.