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)

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Formula

## 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.

Esempio Risolto

A 10 kg mass on a spring with stiffness 10,000 N/m.

  1. 01omega_n = sqrt(10000 / 10) = sqrt(1000) = 31.623 rad/s
  2. 02f_n = 31.623 / (2*pi) = 31.623 / 6.283 = 5.033 Hz
  3. 03Period = 1 / 5.033 = 0.1987 s