We consider the nonlinear oscillations of a simple spring-magnet system that oscillates in the magnetic field of an inductive coil excited with a dc current. Using the relations for the interaction of a coil and a magnet we obtain the motion equation of the system. The relative strengths of the terms of this equation can be adjusted easily by varying the coil excitation current. Both the elastic constant and the shape of the potential energy function of the system can therefore be modified by varying that current. It is shown and demonstrated that this system is a case of anharmonic oscillations in a double-well potential. This nonlinear oscillator can be easily assembled with commonly available laboratory components, and monitored with a digital oscilloscope. Its simplicity is to be compared with the setups of many other nonlinear oscillators recently described. This oscillator is ideal for an advanced undergraduate laboratory experiment or for project work. (Contains 7 figures and 1 footnote.)