Natural Frequency Calculator (Spring-Mass System)
Reviewed by Hamza Gujjar, Algorithm Architect & Software Developer
Last updated: July 27, 2026Natural Frequency Calculator
Every mechanical system with mass and stiffness has a natural frequency at which it vibrates freely once disturbed - this calculator computes it for a simple spring-mass system.
Natural Frequency (rad/s) = √(Spring Stiffness / Mass)
Natural Frequency (Hz) = rad/s / (2π)
Example
A 5,000 N/m spring supporting a 2 kg mass:
ωn = √(5,000/2) = 50 rad/s → fn = 7.958 Hz
Why Resonance Matters
Operating a system at or near its natural frequency can cause resonance - a phenomenon where even a small driving force dramatically amplifies vibration amplitude over time, potentially to destructive levels. This is a fundamental design consideration for anything from washing machines to bridges to rotating machinery.
Designing Away From Natural Frequency
Engineers deliberately design rotating machinery, bridges, and structures to keep their normal operating frequency range safely away from calculated natural frequencies - this is exactly why bridges undergo vibration analysis before construction, and why rotating equipment often has a "critical speed" that must be passed through quickly during startup and shutdown rather than operated at continuously.