A non-linear oscillator is a system where the restoring force is not directly proportional to the displacement, meaning its behavior cannot be accurately described by simple linear equations. For example, while a simple pendulum can be approximated as linear for small angles, it becomes non-linear at larger angles. Non-linear oscillators, like a ring pendulum, exhibit oscillation periods that vary with amplitude, unlike linear systems where the period remains constant. The distinction lies in the mathematical representation; linear systems follow a straightforward relationship, while non-linear systems involve more complex functions. Understanding these differences is crucial for analyzing the dynamics of systems like the ring pendulum.
