  Strongly confined colloidal dispersions under shear can exhibit a variety of
dynamical phenomena, including depinning transitions and complex structural
changes. Here, we investigate the behaviour of such systems under pure
oscillatory shearing with shear rate $\dot{\gamma}(t) = \dot{\gamma}_0
\cos(\omega t)$, as it is a common scenario in rheological experiments. The
colloids' depinning behaviour is assessed from a particle level based on
trajectories, obtained from overdamped Brownian Dynamics simulations. The
numerical approach is complemented by an analytic one based on an effective
single-particle model in the limits of weak and strong driving. Investigating a
broad spectrum of shear rate amplitudes $\dot{\gamma}_0$ and frequencies
$\omega$, we observe complete pinning as well as temporary depinning behaviour.
We discover that temporary depinning occurs for shear rate amplitudes above a
frequency-dependent critical amplitude $\dot{\gamma}_0^\mathrm{crit}(\omega)$,
for which we attain an approximate functional expression. For a range of
frequencies, approaching $\dot{\gamma}_0^\mathrm{crit}(\omega)$ is accompanied
by a strongly increasing settling time. Above
$\dot{\gamma}_0^\mathrm{crit}(\omega)$, we further observe a variety of
dynamical structures, whose stability exhibits an intriguing ($\dot{\gamma}_0,
\omega$) dependence. This might enable new perspectives for potential control
schemes.
