Initial release condition dependent decoupling motion of a Wilberforce pendulum in the case of near resonance

Abstract

Abstract The vertical and angular oscillation of a Wilberforce pendulum was found to be coupled in the case of resonance. Many studies have discussed the effects of the physical properties of a Wilberforce pendulum on coupled motion. In this article, we mainly study the influence of initial release conditions on the coupled motion of a Wilberforce pendulum in the near resonance case. The experimental results clearly exhibit that the coupled motion phenomenon depends on the initial release condition. Theoretical calculation further demonstrates that the coupled strength between two normal modes is determined by the ratio of initial angular to vertical displacement in the case of near resonance. The experimental results also verify the calculated variation of decoupling coefficient with this displacement ratio. Our study indicates that even in the case of resonance, the motion of a Wilberforce pendulum is probably decoupled at a given initial release condition. Complete decoupled motion is found to appear only when the damping coefficients in vertical and angular motion generate equal energy dissipation rates. The corresponding decoupling phenomenon in the case of resonance, occurs when the initial release energy of vertical and angular motion is equal.