Calculadora Avanzada de Frecuencia Natural Gratis
Análisis avanzado de frecuencia natural con múltiples grados de libertad y amortiguamiento. Para sistemas complejos.
Frecuencia Natural (omega_n)
31.623 rad/s
Natural Frequency (omega_n) vs Spring Stiffness (k)
Fórmula
## 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.
Ejemplo Resuelto
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
Preguntas Frecuentes
Why is natural frequency important?
Resonance occurs when an external forcing frequency matches the natural frequency, causing large amplitude oscillations. Engineers must ensure that operating frequencies are sufficiently far from natural frequencies to avoid resonance.
How does damping affect the natural frequency?
Damping does not change the natural frequency omega_n, but the actual oscillation frequency (damped frequency) is omega_d = omega_n × sqrt(1 - zeta²), which is always less than omega_n.
What about systems with multiple degrees of freedom?
Multi-DOF systems have multiple natural frequencies (modes). The lowest is called the fundamental frequency. Modal analysis or eigenvalue methods are used to find all natural frequencies.
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