In a Stern-Gerlach experiment, the spatial trajectory of a particle traversing a magnetic-field gradient serves as a detector of its spin state. This paper considers the implications of adding a harmonic restoring potential to the Stern-Gerlach experiment. The behavior of such systems is shown to resemble that of a ``folded'' Stern-Gerlach experiment, in that the linear spatial trajectory of the Stern-Gerlach experiment becomes folded into the cyclic phase-space trajectory of the oscillator. Under appropriate circumstances, the coupling between the spin and the oscillator is shown to be sufficiently strong that it might find practical application as the basis of a magnetic resonance imaging device.