固有频率计算器 — 公式
## 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.
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.
计算示例
A 5 kg mass on a spring with stiffness 10,000 N/m.
- omega_n = sqrt(10000 / 5) = sqrt(2000) = 44.72 rad/s
- f_n = 44.72 / (2 x 3.1416) = 7.12 Hz
- T = 1 / 7.12 = 0.1405 s