固有频率计算器 — 公式
## 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.
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.
计算示例
A 10 kg mass on a spring with stiffness 10,000 N/m.
- omega_n = sqrt(10000 / 10) = sqrt(1000) = 31.623 rad/s
- f_n = 31.623 / (2*pi) = 31.623 / 6.283 = 5.033 Hz
- Period = 1 / 5.033 = 0.1987 s