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:
- k — 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.
Professional portable balancers, vibration analyzers, and condition monitoring systems used in 50+ countries. Identify resonance problems and balance rotors on-site.
Nikolai Shelkovenko
Nikolai Shelkovenko is a vibration analysis engineer and the founder and CEO of Vibromera. For more than 15 years he has balanced rotating equipment in the field rather than on a test bench: mulchers, industrial fans, crushers, centrifuges, shafts and spindles. That work is what the Balanset instruments grew out of — they were designed as a tool a specialist can carry to the machine and use alone, on site, not as laboratory equipment. Vibromera was founded in 2017 and has been based in Porto, Portugal, since 2023. Development, assembly and support of the Balanset line all happen here. The flagship instrument is the Balanset-1A, a portable analyser for single- and two-plane balancing and for vibration diagnostics. Nikolai is personally involved in customer support, in working through difficult balancing cases and in the development of the software. He works with customers worldwide, in any language.
