Resonances of an oscillating conductive pipe driven by an alternating magnetic field in the presence of a static magnetic field

A short conducting pipe that hangs from a weak spring is forced to oscillate by the magnetic field of a surrounding coaxial coil that has been excited by a low-frequency current source in the presence of an additional static magnetic field. Induced oscillating currents appear in the pipe. The pipe motion becomes damped by the dragging forces between the induced currents and the static field. This oscillating system presents an interesting set of properties. To start with, it is not a magnet interacting with the oscillating field of a coil. The oscillating pipe is not even a ferromagnet. It is a new and conceptually rich case of a damped forced oscillator whose motion differential equation contains coefficients that depend upon a parameter. Here, we present and analytically explain the case of the small amplitude oscillations of this magneto-mechanical system. The ordinary amplitude and phase resonance curves are theoretically derived and confirmed by the set of experimental results presented. This oscillator is inexpensive and simple to set up, does not require sophisticated instrumentation, and with its interesting analytical model, is recommended either as an undergraduate laboratory experiment, as student project work, or even as a demonstration experiment.