Free Natural Frequency Calculator
Calculate the natural frequency of a mass-spring system from stiffness and mass values.
N/m
kg
Natural Frequency (omega_n)
31.623 rad/s
Natural Frequency5.033 Hz
Natural Period0.1987 s
Natural Frequency (omega_n) vs Spring Stiffness (k)
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.
Example Calculation
A 10 kg mass on a spring with stiffness 10,000 N/m.
- 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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