  Using a combination of theory, experiment, and simulation, we revisit the
dynamics of two coupled metronomes on a moving platform. Our experiments show
that the platform's motion is damped by a dry friction force of Coulomb type,
not the viscous linear friction force that has often been assumed in the past.
Prompted by this result, we develop a new mathematical model that builds on
previously introduced models, but departs from them in its treatment of the
friction on the platform. We analyze the model by a two-timescale analysis and
derive the slow-flow equations that determine its long-term dynamics. The
derivation of the slow flow is challenging, due to the stick-slip motion of the
platform in some parameter regimes. Simulations of the slow flow reveal various
kinds of long-term behavior including in-phase and antiphase synchronization of
identical metronomes, phase locking and phase drift of non-identical
metronomes, and metronome suppression and death. In these latter two states,
one or both of the metronomes come to swing at such low amplitude that they no
longer engage their escapement mechanisms. We find good agreement between our
theory, simulations, and experiments, but stress that our exploration is far
from exhaustive. Indeed, much still remains to be learned about the dynamics of
coupled metronomes, despite their simplicity and familiarity.
