Free Natural Frequency Calculator
Determine the natural frequency of a single-degree-of-freedom spring-mass system.
Angular Natural Frequency
44.72 rad/s
Angular Natural Frequency vs Spring Stiffness (k)
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.
Example Calculation
A 5 kg mass on a spring with stiffness 10,000 N/m.
- 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
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