Demonstration of dissipative coupling in feedback coupled pendulum system*

Lab demonstration is considered essential in physics education. One of the ubiquitous undergraduate level demonstrations showcases coherent coupling in a spring-connected pendulum system. Using this simple system, many physics phenomena such as Rabi-oscillation and energy level anti-crossing can be observed. We have constructed a novel double-pendulum system coupled through ampere’s force. The coupling force is continuously self-adjusted using feedback current proportional to the pendulums' relative motion. The system can replicate the coherent coupling effect without a physical spring and is also capable of producing the newly discovered dissipative coupling effect (friction coupled pendulums). The dissipative coupling effect causes system energy level attraction rather than the energy level anti-crossing of a coherent coupling case (spring). When demonstrating pure dissipative coupling, the coupling strength is adjustable between negative dissipation (Gain) and positive dissipation (Loss). This system responds significantly differently under these two conditions. The oscillation amplitude can be damped when the coupling mechanism is adjusted to demonstrate positive dissipation (Loss). In this case, the system tends towards in-phase synchronization. The oscillation amplitude can alternatively be enhanced when the coupling mechanism is tuned to demonstrate negative dissipation (Gain), and this condition leads the system towards anti-phase synchronization. More importantly than its pure research benefit, our coupled pendulum system holds excellent educational value - being suitable for a novel gateway demonstration of dynamic coupling effects for both graduate and undergraduate students.