Natural Frequency Calculator Formula
Understand the math behind the natural frequency calculator. Each variable explained with a worked example.
Formulas Used
Natural Frequency (omega_n)
wn = sqrt(stiffness / mass)Natural Frequency
fn = sqrt(stiffness / mass) / (2 * pi)Natural Period
period = 2 * pi / sqrt(stiffness / mass)Variables
| Variable | Description | Default |
|---|---|---|
stiffness | Spring Stiffness (k)(N/m) | 10000 |
mass | Mass (m)(kg) | 10 |
How It Works
Natural Frequency of a Mass-Spring System
The natural frequency is the frequency at which a system oscillates when displaced and released without external forcing or damping.
Formula
omega_n = sqrt(k / m)
f_n = omega_n / (2*pi)
where k is the spring stiffness (N/m) and m is the mass (kg). This is the fundamental relationship in vibration analysis and control systems design.
Worked Example
A 10 kg mass on a spring with stiffness 10,000 N/m.
stiffness = 10000mass = 10
- 01omega_n = sqrt(10000 / 10) = sqrt(1000) = 31.623 rad/s
- 02f_n = 31.623 / (2*pi) = 31.623 / 6.283 = 5.033 Hz
- 03Period = 1 / 5.033 = 0.1987 s
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Open Natural Frequency Calculator