## The mathematical definition of non-linearity contains two important features:A) A small change in input may produce an incommensurably large change in response. B) The superposition principle does not hold. There are a couple of ways to say what this means. One way is to compare a non-linear system to a linear system like a vibrating violin string. The vibrating string has a motion that is the sum of many simpler contributing motions, i.e. the harmonics of the string. The motions involved in non-linear systems are not simply combinations of a bunch of simpler motions. Another way is to look at the response of a non-linear system to some kind of vibrating input. A linear system always responds by vibrating at the same frequency as the input. A non-linear system does not usually or necessarily respond at the same frequency as the input. |

© The Exploratorium, 1996

## The mathematical definition of non-linearity contains two important features:A) A small change in input may produce an incommensurably large change in response. B) The superposition principle does not hold. There are a couple of ways to say what this means. One way is to compare a non-linear system to a linear system like a vibrating violin string. The vibrating string has a motion that is the sum of many simpler contributing motions, i.e. the harmonics of the string. The motions involved in non-linear systems are not simply combinations of a bunch of simpler motions. Another way is to look at the response of a non-linear system to some kind of vibrating input. A linear system always responds by vibrating at the same frequency as the input. A non-linear system does not usually or necessarily respond at the same frequency as the input. |

© The Exploratorium, 1996