Isochronous oscillations using simple circular hoops

We propose a simple model of an isochronous oscillator consisting of three circular hoops of the same radius. Two of them are identical hoops of negligible mass, and a third one is a Littlewood’s hoop (a circular hoop of negligible mass with a particle of finite mass embedded on its rim) of the same radius placed over the other two hoops and capable of rolling against them without slipping. When released from rest over a horizontal plane from a non-equilibrium configuration, the whole three-hoop system rolls back and forth over the said plane, where the time period of this oscillation is independent of its amplitude, thereby exhibiting the iconic isochronous property.