Natural Frequency Calculator
Calculate the natural frequency of a mass-spring system from stiffness and mass values.
प्राकृतिक आवृत्ति (omega_n)
31.623 rad/s
Natural Frequency (omega_n) vs Spring Stiffness (k)
सूत्र
## 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.
हल किया गया उदाहरण
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
अक्सर पूछे जाने वाले प्रश्न
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.
सीखें