Some of the unusual behavior of mechanical and wave oscillations driven to high amplitude will be demonstrated. A bent tuning curve, where the resonant frequency of an oscillation increases with increasing response amplitude, and hysteresis, will be shown with a driven rubber band. Parametric excitation, where a parameter in the equation of motion is oscillated rather than a driving force applied, will be shown with a pendulum. The pendulum can also display a doubly bent tuning curve. The pendulum, when inverted, can display parametric stabilization. Two organ pipes singing at slightly different frequencies, will interact and sing at identical frequencies when brought close enough to each other, displaying phase locking. A trough of water oscillated vertically shows parametrically excited waves first described by Michael Faraday. Pairs of modes of these waves can interact with a driven mode to convert the driving frequency of the vertical oscillations to another incommensurate (irrationally related) frequency, in a phenomenon called quasiperiodicity. The trough can also display a non-propagating soliton that acts somewhat like a particle.