# Mass on a spring

A spring pulls with force F = -kx. The period depends on mass and stiffness, T = 2 pi sqrt(m/k), not on amplitude.

Physics (university) · Part 05: Oscillations and waves · Card 3 of 11 · Last updated 2026-10-19

## Analogy

A stiffer spring bounces faster, a heavier mass bounces slower.

## Example

**Spring period**

T = 2 pi sqrt(m / k)
T = 2 pi sqrt(0.5 / 200)
T = 0.314 s

## In practice

A 0.5 kg mass on a 200 N/m spring takes about 0.31 s per cycle.

## Practice

### Flashcards

- **What does the period of a mass on a spring depend on?** The mass and the spring constant, not the amplitude.

## Questions people ask

### Does gravity change the period of a vertical spring?

No. Gravity only shifts the equilibrium point lower, because the spring stretches until force balances weight. The oscillation about that new point still has period 2 pi sqrt(m/k). That is why the same spring has the same period on the Moon.

### What is the spring constant?

The spring constant k measures stiffness in newtons per metre. A spring with k = 200 N/m needs 200 N to stretch it by 1 m. Hooke's law says force equals k times the stretch, as long as the spring is not stretched beyond its elastic limit.

## Related concepts

- [Simple harmonic motion](https://studyvisually.com/learn/science/physics-university/physics-university-part-5/physics-university-part-5-concept-1)
- [Period and frequency](https://studyvisually.com/learn/science/physics-university/physics-university-part-5/physics-university-part-5-concept-2)
- [Simple pendulum](https://studyvisually.com/learn/science/physics-university/physics-university-part-5/physics-university-part-5-concept-4)
- [Resonance](https://studyvisually.com/learn/science/physics-university/physics-university-part-5/physics-university-part-5-concept-5)

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