---
tag: 2NHWCM0DK8
kind: concept
name: Relaxation oscillation
msc: [34C26, "34E15"]
specializes: [0AA97XA70K]
sources:
  - url: https://en.wikipedia.org/wiki/Relaxation_oscillator
---

## Summary

A relaxation oscillation is a periodic motion that alternates long phases of slow change with short, abrupt jumps.
It arises in systems with two time scales, where one variable moves much faster than the other.
Examples include the [[van der Pol oscillator|WE89NFZ84Q]] with a large parameter, electronic circuits that charge and discharge a capacitor, and models of nerve impulses.
See the [[definition|JCMXX84BWT]].

## Explanations

### L1 human

Picture a bucket under a tap that tips over and empties when it is full, then slowly fills again.
The filling is slow and the tipping is sudden, and the cycle repeats with a fixed period.
The graph of such a motion against time looks like a series of plateaus and steep drops rather than a smooth sine wave.
The period is set mainly by the slow phases, since the jumps take almost no time.