Question

What is the damped natural frequency (in rad/s) of a second order system whose undamped natural frequency is 25 rad/s and has a damping ratio of 0.3?

Answer 1

Answer:

damped natural frequency = 23.84 rad/s

Explanation:

given data

damping ratio = 0.3

undamped natural frequency = 25 rad/s

to find out

damped natural frequency of a second order system

solution

we know that if damping ratio is = 0

then it is undamped system

and if damping ratio is > 1

then it is overdamped system

and  and if damping ratio is ≈ 1

then it is critical damped system

so damped natural frequency of a second order system formula is

damped natural frequency = wn × $\sqrt{1-r^2}$

here wn is undamped natural frequency and r is damping ratio

damped natural frequency = 25 × $\sqrt{1-0.3^2}$

damped natural frequency = 23.84 rad/s