Natural Frequency Calculator Formula
Understand the math behind the natural frequency calculator. Each variable explained with a worked example.
Formulas Used
Angular Natural Frequency
omega_n = sqrt(spring_k / mass)Natural Frequency
freq_hz = sqrt(spring_k / mass) / (2 * pi)Natural Period
period = 2 * pi / sqrt(spring_k / mass)Variables
| Variable | Description | Default |
|---|---|---|
spring_k | Spring Stiffness (k)(N/m) | 10000 |
mass | Mass (m)(kg) | 5 |
How It Works
Natural Frequency of a Spring-Mass System
Every elastic system has a natural frequency at which it tends to vibrate when disturbed.
Formulas
omega_n = sqrt(k / m) (angular frequency in rad/s)
f_n = omega_n / (2 pi) (frequency in Hz)
T = 1 / f_n = 2 pi / omega_n (period in seconds)
Resonance occurs when the excitation frequency matches the natural frequency, leading to large amplitude vibrations that can cause structural failure.
Worked Example
A 5 kg mass on a spring with stiffness 10,000 N/m.
spring_k = 10000mass = 5
- 01omega_n = sqrt(10000 / 5) = sqrt(2000) = 44.72 rad/s
- 02f_n = 44.72 / (2 x 3.1416) = 7.12 Hz
- 03T = 1 / 7.12 = 0.1405 s
Ready to run the numbers?
Open Natural Frequency Calculator