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This Demonstration illustrates the behavior of a frictionless bead sliding on a circular hoop as the hoop is rotated about a horizontal axis tangent to the bottom of the hoop. Such a device can be built and used to illustrate the principle of the Paul rf ion trap. In the ideal case, the bead's motion is described exactly by Mathieu's equation. However, the behavior of the bead is very sensitive to small perturbations of the apparatus. In this Demonstration, you can observe the effect of increasing the initial displacement of the bead, as well as slightly tilting the rotation axis from the horizontal.
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