Take-off and landing of point mass from an oscillating plate

As a preliminary analysis, we calculate and show in the figure the time trajectory of a single particle taking off from a flat vibrating substrate, where we use a sinusoidal oscillation (Γg/ω2)cosωt with the normalized coordinates φ≡ωt and z~≡z/(Γg/ω2) to eliminate the explicit dependence on frequency. The normalized velocity of impact upon landing, νrel~, is also numerically solved as a function f(Γ).

Local analyses of one particle taking off from an oscillating substratat various values of Γ, and the impact speeds upon landing.