The formula to calculate the Damped Natural Frequency is:
\[ \omega_d = \omega_n \sqrt{1 - \zeta^2} \]
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.
Let's assume the following values:
Using the formula:
\[ \omega_d = 23 \sqrt{1 - 0.1^2} = 22.8847110534523 \]
| 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 |