Vibration Natural Frequency Calculator

Summary

Enter spring stiffness, mass, and optional damping to get the natural and damped frequencies of a single-degree-of-freedom system.

How it works

1. Enter the spring stiffness k (N/m) and mass m (kg).
2. Optionally enter the damping coefficient c (N·s/m) to compute the damped frequency.
3. Click Calculate — the tool applies fn = (1/2π)·√(k/m) for the undamped natural frequency.
4. The critical damping coefficient cc = 2·√(k·m) is computed, then ζ = c/cc for the damping ratio.
5. Damped natural frequency fd = fn·√(1−ζ²) is shown when ζ < 1 (underdamped system).
6. The mode shape panel describes the physical motion type based on your damping ratio.

Use cases

• Mechanical engineers sizing isolators to avoid resonance with equipment.
• Structural analysts checking floor or bridge natural frequencies against operating loads.
• Students verifying vibration textbook problems for SDOF systems.
• Designers comparing undamped and damped responses to choose the right dashpot.
• Quality engineers troubleshooting vibration failures in rotating machinery.
• Educators demonstrating the effect of damping ratio on oscillatory behavior.

Frequently Asked Questions