  We discuss a classical nonlinear oscillator, which is proved to be a
superintegrable system for which the bounded motions are quasiperiodic
oscillations and the unbounded (scattering) motions are represented by
hyperbolic functions. This oscillator can be seen as a position-dependent mass
system and we show a natural quantization prescription admitting a
factorization with shape invariance for the $n=1$ case, and then the energy
spectrum is found. Other isochronous systems which can also be considered as a
generalization of the harmonic oscillator and admit a nonstandard Lagrangian
description are also discussed.
