Natural Frequency in a Mass-Spring Model: Keep Mass and Stiffness Together

Define the simplified model

For an undamped linear mass-spring model, natural angular frequency is √(k/m), and frequency in cycles per second is √(k/m)/(2π). Primary reference: simple harmonic motion.

The effective mass and stiffness must describe the same motion direction. A motor nameplate speed is not an input to this equation. A distributed machine structure may have several modes, so this calculation represents a defined approximation rather than its complete vibration behavior.

A hypothetical comparison

Assume a fictional moving assembly has effective mass 4 kg and stiffness 4,000 N/m in one direction. The angular frequency is √1,000 = 31.62 rad/s, corresponding to approximately 5.03 Hz. Doubling mass alone gives approximately 3.56 Hz; doubling stiffness alone gives approximately 7.12 Hz.

The two changes have opposite effects even though each doubles one input. Keep the original direction and boundary assumptions beside every row. If an added bracket changes both stiffness and participating mass, neither one-input result predicts the new assembly. These invented values describe no HM machine.

Prepare a frequency question

Ask what moves together, where the restoring force comes from and which supports belong to the model. Record whether the proposed stiffness is translational or rotational before choosing units. A measured peak requires its own interpretation with forcing and damping evidence.

Use this worksheet to check a model comparison before requesting a detailed assessment: mass, stiffness, direction, support condition and frequency convention. Preserve radians per second and hertz in separate columns so a numerical conversion does not look like a change in physical behavior.

Customer Questions

Primary References

These references support the technical principles discussed in this guide. The worked examples and review questions are educational.

• Primary reference: simple harmonic motion