Damped Natural Frequency
Find the oscillation frequency of an underdamped second-order mode.
Try this formula
Calculate damped angular natural frequency or choose another supported quantity.
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Try this formula
Calculate damped angular natural frequency or choose another supported quantity.
Use decimals or scientific notation, such as 1.2e3. Calculations update as you type.
Damped angular natural frequency
Enter the known values to see the result.
Use a stable, linear, underdamped second-order model with 0 < ζ < 1. Natural frequency is angular frequency in rad/s, not cycles per second. At critical or overdamping there is no oscillatory damped frequency described by this formula.
Difficulty
Intermediate
Read time
5 min
Prerequisites
Basic algebra and introductory dynamic systems
Source
Donney Fan — MECH 466 — Automatic ControlReference equation: Second Order System — Underdamped Case. FormuLab wrote new explanations, assumptions, applications, and numerical examples.
Definition
Viscous damping reduces oscillation frequency below the undamped natural frequency. As the damping ratio approaches one, the oscillatory component disappears.
Variables & Units
| Symbol | Meaning | Units |
|---|---|---|
| Damped angular natural frequency | ||
| Undamped angular natural frequency | ||
| Damping ratio |
Real-World Applications
Vibration response
Estimate the oscillation rate of a damped mode.
Control models
Interpret the imaginary part of a second-order pole pair.
Worked Example
Problem
For ωn = 10 rad/s and ζ = 0.2, find the damped natural frequency.
Given
Solution
Final Answer
Contents
Info
Tools
Source & review
Reference equation: Second Order System — Underdamped Case. FormuLab wrote new explanations, assumptions, applications, and numerical examples.
Assumptions
- • Use a stable, linear, underdamped second-order model with 0 < ζ < 1.
- • Natural frequency is angular frequency in rad/s, not cycles per second.
- • At critical or overdamping there is no oscillatory damped frequency described by this formula.
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