The parametric oscillations of an oscillator driven electromagnetically are presented. The oscillator is a conductive pipe hung from a spring, and driven by the oscillating magnetic field of a surrounding coil in the presence of a static magnetic field. It is an interesting case of parametric oscillations since the pipe is neither a magnet nor a ferromagnet, and because the driving and the damping forces are functions of the "magnet-to-pipe" distance. We develop an analytical model of the oscillator that leads to a new kind of Mathieu equation with nonlinear terms of third order in the oscillator position, and on the product of the squared position times the first derivative of the position function. We show how the oscillations evolve as the frequency is varied up to the saturation regime and present ample experimental evidence of the parametric nature of our oscillator. Because of its peculiarities and their advanced scientific and technological applications, parametric oscillations are very important for physicists and engineers at both senior undergraduate and graduate levels. This oscillator is very easy to set up and provides an excellent opportunity to learn all facets of parametric oscillations at both levels. (Contains 10 figures.)