  We apply a toy model based on 'pendulum waves' to gas sloshing in galaxy
clusters. Starting with a galaxy cluster potential filled with a hydrostatic
intra-cluster medium (ICM), we perturb all ICM by an initial small,
unidirectional velocity, i.e., an instantaneous kick. Consequently, each parcel
of ICM will oscillate due to buoyancy with its local Brunt-V\"ais\"al\"a (BV)
period, which we show to be approximately proportional to the cluster radius.
The oscillation of gas parcels at different radii with different periods leads
to a characteristic, outwards-moving coherent pattern of local compressions and
rarefactions; the former form the sloshing cold fronts (SCFs). Our model
predicts that SCFs (i) appear in the cluster centre first, (ii) move outwards
on several Gyr timescales, (iii) form a staggered pattern on opposite sides of
a given cluster, (iv) each move outwards with approximately constant speed; and
that (v) inner SCFs form discontinuities more easily than outer ones. These
features are well known from idealised (magneto)-hydrodynamic simulations of
cluster sloshing. We perform comparison hydrodynamic+N-body simulations where
sloshing is triggered either by an instantaneous kick or a minor merger.
Sloshing in these simulations qualitatively behaves as predicted by the toy
model. However, the toy model somewhat over-predicts the speed of sloshing
fronts, and does not predict that inner SCFs emerge with a delay compared to
outer ones. In light of this, we identify the outermost cold front, which may
be a 'failed' SCF, as the best tracer of the age of the merger that set a
cluster sloshing.
