# Statistics of injected power on a bouncing ball

# subjected to a randomly vibrating piston

**A. Garcia-Cid**^{1}**, P.
Gutiérrez**^{1}, C. Falcon^{1}, S. Aumaître^{2}
and E. Falcon^{3}

^{1} FCFM, Universidad del Chile,
Casilla 487-3, Santiago, Chile

^{2} CEA-Saclay, Sphynx, DSM, UMR 3680 CNRS, F-91 191
Gif-sur-Yvette, France

^{3} Univ Paris Diderot, Sorbonne Cité, MSC, CNRS, UMR
7057, F-75 013 Paris, France

### Reference: Physical
Review E 92, 032915 (2015)

**Abstract: **

We present an experimental
study on the statistical properties of the injected power needed
to maintain an inelastic ball bouncing constantly on a randomly
accelerating piston in the presence of gravity. We compute the
injected power at each collision of the ball with the moving
piston by measuring the velocity of the piston and the force
exerted on the piston by the ball. The probability density
function of the injected power has its most probable value close
to zero and displays two asymmetric exponential tails, depending
on the restitution coefficient, the piston acceleration, and its
frequency content. This distribution can be deduced from a
simple model assuming quasi-Gaussian statistics for the force
and velocity of the piston.

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