Title: Sub-harmonic Injection Locking in Metronomes,
Abstract: In this paper, we demonstrate sub-harmonic injection locking (SHIL) in
mechanical metronomes. To do so, we first formulate metronome's physical
compact model, focusing on its nonlinear terms for friction and the escapement
mechanism. Then we analyze metronomes using phase-macromodel-based techniques
and show that the phase of their oscillation is in fact very immune to periodic
perturbation at twice its natural frequency, making SHIL difficult. Guided by
the phase-macromodel-based analysis, we are able to modify the escapement
mechanism of metronomes such that SHIL can happen more easily. Then we verify
the occurrence of SHIL in experiments. To our knowledge, this is the first
demonstration of SHIL in metronomes; As such, it provides many valuable
insights into the modelling, simulation, analysis and design of nonlinear
oscillators. The demonstration is also suitable to use for teaching the subject
of injection locking and SHIL.