# Simple pendulum

A mass on a string swinging through small angles. Its period T = 2 pi sqrt(L/g) depends on length, not mass.

Physics (university) · Part 05: Oscillations and waves · Card 4 of 11 · Last updated 2026-10-19

## Analogy

A playground swing with a longer chain swings slower.

## Example

**1 m pendulum**

T = 2 pi sqrt(L / g)
T = 2 pi sqrt(1 / 9.8)
T = 2.01 s

## In practice

A 1.00 m pendulum swings once every 2.0 s on Earth.

## Practice

### Flashcards

- **Does a pendulum's period depend on its mass?** No. It depends on length and g only.

### Interview questions

**A pendulum clock runs slow on a mountain top. Explain why.**

- Period depends on g
- g is slightly smaller at altitude
- Smaller g gives longer period

## Questions people ask

### Why does the pendulum formula only work for small angles?

For small angles, the restoring force is nearly proportional to the angle, which gives SHM. At large angles the force grows more slowly, so the period increases. Below about 10 degrees the formula is accurate to within about 0.2 percent, which is fine for exams.

### How can a pendulum measure g?

Time many swings of a pendulum of known length, find the period T, then rearrange T = 2 pi sqrt(L/g) to get g = 4 pi squared L over T squared. A 1.00 m pendulum with a 2.01 s period gives g of about 9.77 m/s squared.

## Related concepts

- [Period and frequency](https://studyvisually.com/learn/science/physics-university/physics-university-part-5/physics-university-part-5-concept-2)
- [Simple harmonic motion](https://studyvisually.com/learn/science/physics-university/physics-university-part-5/physics-university-part-5-concept-1)
- [Mass on a spring](https://studyvisually.com/learn/science/physics-university/physics-university-part-5/physics-university-part-5-concept-3)
- [Resonance](https://studyvisually.com/learn/science/physics-university/physics-university-part-5/physics-university-part-5-concept-5)

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