  Colloidal particles moving in a fluid interact via the induced velocity
field. The collective dynamic state for a class of actively forced colloids,
driven by harmonic potentials via a rule that couples forces to configurations,
to perform small oscillations around an average position, is shown by
experiment, simulation and theoretical arguments to be determined by the
eigenmode structure of the coupling matrix. It is remarkable that the dynamical
state can therefore be predicted from the mean spatial configuration of the
active colloids, or from an analysis of the fluctuations near equilibrium. This
has the surprising consequence that while 2 particles, or polygonal arrays of 4
or more colloids, synchronize with the nearest neighbors in anti-phase, a
system of 3 equally spaced colloids synchronizes in-phase. In the absence of
thermal fluctuations, the stable dynamical state is predominantly formed by the
eigenmode with longest relaxation time.
