Second order systems

Question 1

How can natural frequency and the damping factor be determined via comparison?

Answer 1

Using the equation AWn^2 / s^2 +szWn + Wn^2
and the TF of a second order system
(typically bo/ s^2 +a1s + a2)

Question 2

How can omega and zeta be determined from the time response?

Answer 2

1. consider 2 time points where the sinusoid is at its maximum
2. ∆t = 2π / wd
3. Assess the ratio of the peak magnitudes