  The power spectrum of displacement fluctuation of beads in the air-fluidized
granular system is measured by a novel NMR technique of modulated gradient
spin-echo. The results of measurement together with the related spectrum of the
velocity fluctuation autocorrelation function fit well to an empiric formula
based on to the model of bead caging between nearest neighbours; the cage
breaks up after a few collisions \cite{Menon1}. The fit yields the
characteristic collision time, the size of bead caging and the diffusion-like
constant for different degrees of system fluidization. The resulting mean
squared displacement increases proportionally to the second power of time in
the short-time ballistic regime and increases linearly with time in the
long-time diffusion regime as already confirmed by other experiments and
simulations.
