Calculate the resonance frequency

Question

A second order system has a natural frequency 32 rads/s and a damping ratio 0.48.

calculate the resonance frequency.

Answer 1

The resonance frequency here can also be called the "damped natural frequency." The natural frequency, f_n = 32 rad/s, is the natural frequency of the system when it is free from damping. The relationship between undamped and damped natural frequency is as follows:

ω_d = ω_n ( 1-ς² )^1/2

So: ω_d = (32 rad/s) ( 1-0.48² )^1/2

ω_d = 28.073 rad/s