Energy dissipation for two particles in a vertically vibrating channel

The “chattering ball” problem examined in the 1980’s consisted of a particle bouncing on a vertically vibrating plate under gravity as a simple nonlinear system that demonstrates rich dynamical behaviors. Here, we study the energy dissipation of two identical particles free to collide in a vertical channel in a shaken experiment. Both spherical particles are Delrin with a diameter of d=5.0 mm. Multiple cases are considered with driving frequencies, f, ranging from 23 to 32 Hz and acceleration magnitudes, Γ, from 1.78 to 3.53 g. The positions and velocities of each particle from the experiment are extracted by high speed imaging. The energy dissipation is evaluated in both the lab frame and the center of mass frame. The experimental results show that most data in the mechanical energy before and after collision cluster around a straight line with a slope slightly smaller than unity. The experimental results suggest that the mechanical energy after collision depends linearly on the mechanical energy before collision in most cases. However, some data indicates an occasional transfer of kinetic energy from the translational to the rotational degree of freedom and vice versa.