  We present an experimental study of the collective dipole oscillation of a
spin-orbit coupled Bose-Einstein condensate in a harmonic trap. Dynamics of the
center-of-mass dipole oscillation is studied in a broad parameter region, as a
function of spin-orbit coupling parameters as well as oscillation amplitude.
Anharmonic properties beyond effective-mass approximation are revealed, such as
amplitude-dependent frequency and finite oscillation frequency at place with
divergent effective mass. These anharmonic behaviors agree quantitatively with
variational wave-function calculations. Moreover, we experimentally demonstrate
a unique feature of spin-orbit coupled system predicted by a sum-rule approach,
stating that spin polarization susceptibility--a static physical quantity--can
be measured via dynamics of dipole oscillation. The divergence of polarization
susceptibility is observed at the quantum phase transition that separates
magnetic nonzero-momentum condensate from nonmagnetic zero-momentum phase. The
good agreement between the experimental and theoretical results provides a
bench mark for recently developed theoretical approaches.
