Damped Natural Frequency Calculator

Calculate Damped Natural Frequency





Formula

The formula to calculate the Damped Natural Frequency is:

\[ \omega_d = \omega_n \sqrt{1 - \zeta^2} \]

Definition

Damped Natural Frequency is the frequency at which a resonant mechanical structure will continue oscillating if set in motion and left to its own devices. The Natural Frequency of Oscillation is the frequency at which a system oscillates when disturbed from its equilibrium position. The Damping Ratio is the ratio with which any signal gets decayed in a control system.

Example Calculation

Let's assume the following values:

Using the formula:

\[ \omega_d = 23 \sqrt{1 - 0.1^2} = 22.8847110534523 \]

Conversion Chart

Natural Frequency of Oscillation (ωn) Damping Ratio (ζ) Damped Natural Frequency (ωd)
20 0.1 19.899748742132399
22 0.1 21.889723616345638
24 0.1 23.879698490558880
26 0.1 25.869673364772119
28 0.1 27.859648238985358
30 0.1 29.849623113198600