  A description of the dynamical response of uniformly trapped Bose-Einstein
condensates (BECs) to oscillating external gravitational fields is developed,
with the inclusion of damping. Two different effects that can lead to the
creation of phonons in the BEC are identified; direct driving and parametric
driving. Additionally, the oscillating gravitational field couples phonon
modes, which can lead to the transition of excitations between modes. The
special case of the gravitational field of a small, oscillating sphere located
closely to the BEC is considered. It is shown that measurement of the effects
may be possible for oscillating source masses down to the milligram scale, with
a signal to noise ratio of the order of 10. To this end, noise terms and
variations of experimental parameters are discussed and generic experimental
parameters are given for specific atom species. The results of this article
suggest the utility of BECs as sensors for the gravitational field of very
small oscillating objects which may help to pave the way towards gravity
experiments with masses in the quantum regime.
