  We investigate the dynamics of microcapsules in linear shear flow within a
reduced model with two degrees of freedom. In previous work for steady shear
flow, the dynamic phases of this model, i.e. swinging, tumbling and
intermittent behaviour, have been identified using numerical methods. In this
paper, we integrate the equations of motion in the quasi-spherical limit
analytically for time-constant and time-dependent shear flow using matched
asymptotic expansions. Using this method, we find analytical expressions for
the mean tumbling rate in general time-dependent shear flow. The capsule
dynamics is studied in more detail when the inverse shear rate is harmonically
modulated around a constant mean value for which a dynamic phase diagram is
constructed. By a judicious choice of both modulation frequency and phase,
tumbling motion can be induced even if the mean shear rate corresponds to the
swinging regime. We derive expressions for the amplitude and width of the
resonance peaks as a function of the modulation frequency.
