Spring Mass Frequency Calculator

Calculator Inputs

Spring Constant

Spring Constant Unit

Mass

Mass Unit

Damping Ratio (ζ)

Initial Amplitude

Amplitude Unit

Phase Angle (degrees)

Gravity (m/s²)

Graph Cycles

Graph Points

Reset

Formula Used

Natural angular frequency: ωₙ = √(k / m)

Here, k is spring constant and m is mass.

Natural frequency: fₙ = ωₙ / 2π

Period: T = 1 / fₙ

Damped angular frequency for underdamped motion: ωd = ωₙ √(1 - ζ²)

Damped frequency: fd = ωd / 2π

Critical damping coefficient: cc = 2 √(km)

Actual damping coefficient: c = ζ × cc

Static deflection: δ = mg / k

Stored energy: E = ½kA²

Peak spring force: F = kA

This calculator converts all inputs to SI units first, performs the calculations, then reports the important motion and system parameters.

How to Use This Calculator

Enter the spring constant and choose its unit.
Enter the attached mass and select the mass unit.
Add damping ratio if the system is damped. Use zero for undamped motion.
Enter initial amplitude and the unit you want the graph to display.
Optionally set phase angle, graph cycles, and point count.
Click Calculate Frequency to show results above the form.
Review the table, chart, and derived quantities such as period, energy, and damping coefficients.
Use the CSV or PDF buttons to export the generated result summary.

Example Data Table

Case	Spring Constant	Mass	Damping Ratio	Amplitude	Natural Frequency	Period
Bench Test A	200 N/m	2 kg	0.02	0.05 m	1.5915 Hz	0.6283 s
Bench Test B	350 N/m	5 kg	0.10	0.03 m	1.3310 Hz	0.7513 s
Bench Test C	1200 N/m	12 kg	0.20	0.01 m	1.5915 Hz	0.6283 s

FAQs

1. What is spring mass frequency?

It is the rate at which a mass on a spring oscillates. It depends mainly on spring stiffness and attached mass, not on gravity for the ideal frequency value.

2. What increases the natural frequency?

A stiffer spring raises natural frequency. A lighter mass also raises it. Increasing stiffness and reducing mass both make the system oscillate faster.

3. Why does a larger mass lower frequency?

More mass increases inertia. The spring needs more time to reverse the motion, so the oscillation slows and the frequency decreases.

4. What is damped frequency?

Damped frequency is the oscillation rate after energy loss is included. For underdamped motion, it is slightly lower than natural frequency because damping reduces the oscillation speed.

5. Can I use non-SI units?

Yes. This calculator accepts common engineering units for spring constant, mass, and amplitude. It converts them internally before calculating the final results.

6. Why does the graph decay over time?

Decay appears when damping ratio is above zero. Damping removes energy from the system, so the motion amplitude gradually reduces as time passes.

7. What happens at a damping ratio of one?

The system becomes critically damped. It returns to equilibrium as quickly as possible without oscillating, so damped frequency is not reported.

8. Is static deflection related to frequency?

Yes. Static deflection reflects how far the spring stretches under weight. It helps describe system stiffness behavior, although frequency is still computed from stiffness and mass.