What is the formula used?

The natural frequency is f = (1 / (2π)) × √(k / m), where k is the spring constant in N/m and m is the mass in kg. Angular frequency ω = √(k/m) in rad/s. Period T = 1/f in seconds.

What units should I use for input?

Enter mass in kilograms (kg) and spring constant in newtons per meter (N/m). The output frequency is in hertz (Hz) and angular frequency in radians per second (rad/s).

What is the difference between Hz and rad/s?

Hertz (Hz) measures cycles per second — how many full oscillations occur each second. Radians per second (rad/s) is angular frequency; they are related by ω = 2πf.

Does damping affect the resonance frequency?

This calculator assumes an undamped system. In real systems with damping, the damped natural frequency is slightly lower: f_d = f × √(1 − ζ²), where ζ is the damping ratio. For most lightly-damped systems the difference is negligible.

Can I use this for a spring with no attached mass?

No — you need both a mass and a spring constant. A spring alone does not oscillate; it is the interaction of the restoring spring force and the inertia of the mass that creates resonance.

How do I find the spring constant of a real spring?

Measure the deflection δ (meters) when a known force F (newtons) is applied; then k = F / δ. Alternatively, hang a known mass, measure the static extension, and use k = mg / δ.

Resonance Frequency System

Name: Resonance Frequency System
Availability: InStock
Author: Nham Vu

Enter mass and spring constant to instantly calculate the natural resonance frequency of a mass-spring system.

System Parameters

Mass (kg)

Mass of the object attached to the spring.

Spring Constant (N/m)

Stiffness of the spring in newtons per meter.

Enter mass and spring constant to see results.

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Summary

Enter mass and spring constant to instantly calculate the natural resonance frequency of a mass-spring system.

How it works

Enter the mass of the object attached to the spring in kilograms.
Enter the spring constant (stiffness) in newtons per meter (N/m).
The tool applies the formula f = (1/2π)√(k/m) to find natural frequency.
Angular frequency ω = √(k/m) is also calculated in radians per second.
Period T = 1/f shows the time for one complete oscillation cycle.
Results update instantly as you type either value.

Use cases

Mechanical engineering design of vibration isolation systems.
Determining if a structure might resonate at a given excitation frequency.
Physics coursework and lab calculations for simple harmonic motion.
Automotive suspension spring selection and tuning.
MEMS sensor design — calculating resonant frequency of micro-cantilevers.
Earthquake engineering — estimating building natural frequencies.
Audio transducer and speaker suspension design.
Quick sanity checks during FEA (finite element analysis) modeling.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu