A granular damper is a container or cavity filled by microscopic particles. When agitated, granular dampers dissipate energy due to inelastic collisions. Therefore, the amplitude of a harmonic spring with an attached granular damper decays in time.

When the influence of gravity is eliminated, one observes a surprising characteristic behavior. Unlike a viscous damper, a granular damper does not lead to an exponential decay in amplitude as a function of time. Instead, it decays almost linearly.

This is true up to a certain residual amplitude. After this point, the decay of the amplitude proceeds much slower. These characteristic features have been reported in a number of publications but remain unexplained. The present paper aims to explain this behavior.

For large amplitudes, we observe a collective motion of the particles, synchronous to the motion of the box. For small amplitudes, a disordered gas-like motion is observed. We find the same dynamical behavior in a steadily driven granular damper. For small amplitudes, we see the gas-like behavior.

For large amplitudes, all particles collapse inelastically onto the wall, twice per period, and get released once the box starts to decelerate. These two regimes are separated by a threshold amplitude, determined by the filling ratio of the container. This similarity suggests to consider the relaxation process as a sequence of steady states,

which is justified as long as the relaxation time is much larger than the period of the oscillation. With this, we can use the previously derived expressions for the energy dissipation in the steady driven system to describe the relaxation. The result is a differential equation describing the decay in amplitude.

This prediction agrees very well with the experimental data. The collect-and-collide damping process continues until the amplitude crosses the threshold where a transition to the gas-like regime occurs and the damping is much weaker. The initial slope of the amplitude and the residual amplitude where the rapid linear decay ceases

are both increasing functions of the filling ratio of the container. Therefore, when applying granular dampers, one has to compromise between efficient damping and final amplitude.