曼妙舞姿--妙妙圈力與波的共伴迴旋 Waves on a Dancing Slinky: An Analysis of its Force and Rotation
The Slinky, a familiar toy, exhibits fascinating dynamics beyond its well-known vertical oscillations. When twisted and released, it undergoes periodic torsional motion accompanied by lateral wave propagation along its coils. This study investigates the coupling mechanism between the Slinky’s torsional oscillation and its wave behavior, aiming to construct a unified physical model describing this phenomenon. By analyzing the system as a torsional oscillator, we derived relationships among its rotational inertia, restoring torque, and oscillation period. Experiments were conducted to measure the lateral and torsional spring constants of individual coils, as well as the kinetic friction between adjacent layers. High-speed imaging and motion tracking were used to record the angular displacement, angular velocity, and lateral wave propagation under varying conditions such as coil number, initial twist angle, and Slinky height. Results show that the Slinky’s angular amplitude decays linearly due to constant kinetic friction torque, while the oscillation period remains nearly identical to that of an undamped system. Moreover, lateral wave speed is independent of the initial torsion, whereas wavelength and frequency vary proportionally and inversely with the initial twist angle, respectively. These findings demonstrate that torsional deformation acts as the driving source of lateral waves, providing a more complete explanation of the Slinky’s intertwined rotational and wave dynamics.