Free Engineering Tool
Natural Frequency Calculator
Calculate the natural frequency of a mass-spring system. Enter mass and spring stiffness to get frequency in Hz, angular frequency, period, equivalent RPM, and static deflection.
Results
Natural Frequency of a Mass-Spring System
The natural frequency of an undamped single-degree-of-freedom mass-spring system:
- കെ — spring stiffness (N/m). If given in N/mm, multiply by 1000.
- m — mass (kg)
Angular Frequency
Period and Static Deflection
Where g = 9.81 m/s² and k is in N/mm for the deflection result in mm.
Practical Example
Given: Machine mass = 150 kg, Total spring stiffness k = 300 N/mm
k in N/m = 300 × 1000 = 300,000 N/m
f_n = (1/2π) × √(300,000/150) = (1/6.2832) × 44.72 = 7.12 Hz
ω_n = 2π × 7.12 = 44.7 rad/s
T = 1/7.12 = 0.140 s
Equivalent RPM = 7.12 × 60 = 427 RPM
δ_static = 150 × 9.81 / 300,000 × 1000 = 4.9 mm
⚠️ Note: Ensure the operating speed is at least 20–30% away from the natural frequency to avoid resonance. If operating near resonance, add damping or modify stiffness/mass.
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