Resonant Frequency and Resonant Peak Values

• For a second order system:

$$w_r=w_n\sqrt{1-2{\zeta }^2}$$

• For an undamped system, $\zeta =0$ and $w_r=w_n$. Peak is infinity

• As $\zeta$ changes:

  

  • Note that this is for plotting the Bode plot ($0.5$ is an approximation; it is $\frac{1}{\sqrt{2}}=0.707$)

• As $\zeta$ increases, the phase transition becomes steeper

Resources

• Understanding Vibration and Resonance