a grand on the emperor is a container a cavity
so i microscopic particles
when agitated
granted access dissipate energy you to invest conditions
therefore the amplitude of harmonics bring with an attachment that damper the case in time
when the influence of brevity is eliminated one observes a surprising characteristic behaviour
unlike of is this temper
i granted amber does not lead to an exponential decay
in amplitude as a function of time
instead
if the case almost linearly
this is true up to a certain residual amplitude
after this point dedicate of the amplitude proceed much lower
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 behaviour in this they really driven going the temporal for
small and q
we see the cost like behavior
a large amplitudes all particles collapsed in the lexically on the more twice the period
and get released once the box starts this elaborate
these two machines are separated by a threshold amplitude determined by the feeling ratio of
the container
dissimilarity suggest to consider the relaxation process as a sequence of statistics 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 what the energy dissipation in this
day degree of the system to describe the relaxation
the results of differential equation describing the decaying amplitude
this prediction agrees very well with the experimental data
the collect and collide damping process continues until the amplitude across a 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 whether rapidly near the case
he says with a function of the feeling ratio of the country
therefore
when applying for another person
one has to compromise between efficient dampening and final amplitude