  We present an experimental study on non-equilibrium dynamics of a spinor
condensate after it is quenched across a superfluid to Mott insulator (MI)
phase transition in cubic lattices. Intricate dynamics consisting of
spin-mixing oscillations at multiple frequencies are observed in time
evolutions of the spinor condensate localized in deep lattices after the
quantum quench. Similar spin dynamics also appear after spinor gases in the MI
phase are suddenly moved away from their ground states via quenching magnetic
fields. We confirm these observed spectra of spin-mixing dynamics can be
utilized to reveal atom number distributions of an inhomogeneous system, and to
study transitions from two-body to many-body dynamics. Our data also imply the
non-equilibrium dynamics depend weakly on the quench speed but strongly on the
lattice potential. This enables precise measurements of the spin-dependent
interaction, a key parameter determining the spinor physics.
