A system of two magnets hung from two vertical springs and oscillating in the hollows of a pair of coils connected in series is a new, interesting and useful example of coupled oscillators. The electromagnetically coupled oscillations of these oscillators are experimentally and theoretically studied. Its coupling is electromagnetic instead of mechanical, and easily adjustable by the experimenter. The coupling of this new coupled oscillator system is determined by the currents that the magnets induce in two coils connected in series, one to each magnet. It is an interesting case of mechanical oscillators with field-driven coupling, instead of mechanical coupling. Moreover, it is both a coupled and a damped oscillating system that lends itself to a detailed study and presentation of many properties and phenomena of such a system of oscillators. A set of experiments that validates the theoretical model of the oscillators is presented and discussed. (Contains 16 figures and 1 footnote.)