Non-linear Oscillations
Oscillatory systems where restoring forces do not obey linear Hooke's law, leading to amplitude-dependent frequency and chaotic behavior.
Governing formula
m (d²x/dt²) + k x + β x³ = 0 (Duffing Equation)
SI unit
Various
In depth
In non-linear systems, frequency changes with oscillation amplitude, and simple superposition no longer holds.
Examples in the real world
Large-amplitude swinging pendulums where $sintheta neq theta$ or non-linear electronic circuits.