Dissipative coupling in mechanical systems

Abstract

We have experimentally demonstrated dissipative coupling in a double pendulum system through two approaches. The proposed experiments are easy to form, relatively budget friendly, and the theoretical calculations are also suitable for the undergraduate level. Our experiments can serve as novel demonstrations for this ubiquitous dynamic coupling effect. In the first approach, our experiments employs Lenz’s effect to couple the pendulums through electromagnetic friction. Our experiment revealed level attraction of two system's modes induced by dissipative coupling effect, which is distinctly different from level repulsion caused by coherent coupling that is well-known through the spring coupled pendulums. The second approach is by a feedback coupling mechanism. It is capable of replicating the spring-coupled pendulums without a physical spring, and also able to produce a dissipative coupling and identical physical phenomena as the first approach. The dissipative coupling strength is typically assumed to be positive values, which corresponds with energy dissipation to the surrounding (loss). This effect brings the system back to the equilibrium state. It showcases oscillation amplitude decay and in-phase synchronization between two pendulums. Nevertheless, the natural generalization allows the coupling strength to have either sign. The feedback coupling mechanism is also capable of demonstrating dissipative coupling with negative coupling strength. Unlike the previous experiments, negative coupling strength leads to different physical dynamics. The system intakes energy from external sources (gain) through the coupling mechanism and pushes the system away from equilibrium. This effect showcases oscillation amplitude enhancement and anti-phase synchronization, which is rare to observe. This work completes the classical mechanical picture of dissipative coupling, and it is inspirational for future work in circuit and cavity magnonic systems. Furthermore, these works also bridge the gap between the cutting-edge condensed matter physics research topics to the classroom knowledge for undergraduate and entry level graduate students in particular.