\[\omega_d=\omega_n\sqrt{1-\zeta^2}\]
Variables
Omd[ωd]damped natural angular frequency (rad/s)
Omn[ωn]undamped natural angular frequency (rad/s)
zeta[ζ]damping ratio
Description
What is this formula?
This formula calculates the damped natural angular frequency of an underdamped vibration system. It shows how damping reduces the oscillation frequency compared with the undamped natural frequency.
When to use it
Use this formula for second-order vibration systems when the damping ratio is less than 1 and the system still oscillates.
Example
Data:
Omn = 20 rad/s
zeta = 0.30
Formula:
Omd=Omn*√(1-zeta²)
Substitution:
Omd=20*√(1-0.30²)
Result:
Omd=19.08 rad/s
Applications
Mechanical vibrations
Suspension systems
Machine dynamics
Control systems
Damped oscillator analysis