Calcolatrice Frequenza Naturale Gratuita

Calcola la frequenza naturale di un sistema massa-molla.

N/m
kg

Angular Natural Frequency

44.72 rad/s

Natural Frequency7.12 Hz
Natural Period0.1405 s

Angular Natural Frequency vs Spring Stiffness (k)

Vedi formula →

Formula

## 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.

Esempio Risolto

A 5 kg mass on a spring with stiffness 10,000 N/m.

  1. 01omega_n = sqrt(10000 / 5) = sqrt(2000) = 44.72 rad/s
  2. 02f_n = 44.72 / (2 x 3.1416) = 7.12 Hz
  3. 03T = 1 / 7.12 = 0.1405 s