Taut-Line Buzzers with Periodic Forcing

Abstract

The time-dependent forcing and work per cycle required to drive sinusoidal spinning of a taut-line buzzer is analytically derived, both on and off resonance, from the nonlinear equation of motion. To test predictions, a model experimental system is constructed and characterized in terms of contraction versus twist angle and damped oscillations. The predicted force profile is then approximately implemented by hand. Nearly sinusoidal motion is observed, and the energy injection per cycle needed to maintain steady state oscillations is found to agree with theory. Additional force profiles are implemented, one to maximize non-sinusoidal response and one to maximize the response per operator effort. With the latter, an Aluminum disk of radius 5~cm and height 0.95~cm was spun at a peak speed of over 11,000~RMP for fifteen minutes. The corresponding hand-powered centrifuge system would required $1.5\times$ more force, twice the power, and triple the time in order to run $90\times$ more samples than prior state-of-art.