How to find damping ratio of a second order system

The distance of the pole from the origin in the s-plane is the undamped natural frequency ωn. The damping ratio is given by ζ = cos (θ).

1. What is damping ratio in second order system?
2. How to find damping ratio of a second order system in Matlab?
3. What are the effects of damping ratio on the response of a second order system?

What is damping ratio in second order system?

Frequency response for second-order systems, for damping ratios ζ = 0.01, 0.11, 0.21 … 1.01; natural frequency ω_n = 1. Note that for low damping there is significant peaking in the frequency response near 1 rad/s. Note that as the damping ratio ζ varies, the pole locations vary as well.

How to find damping ratio of a second order system in Matlab?

[ wn , zeta ] = damp( sys ) returns the natural frequencies wn , and damping ratios zeta of the poles of sys . [ wn , zeta , p ] = damp( sys ) also returns the poles p of sys .

What are the effects of damping ratio on the response of a second order system?

The damping ratio is greater than 1 and the poles are both negative real numbers. The system reaches its steady state without oscillation. As the damping ratio increases, it reaches the steady state slower.