Abstract
We consider the dynamics of a pendulum made of a rigid ring attached to an elastic filament immersed in a flowing soap film. The system shows an oscillatory instability whose onset is a function of the flow speed, length of the supporting string, the ring mass, and ring radius. We characterize this system and show that there are different regimes where the frequency is dependent or independent of the pendulum length depending on the relative magnitude of the added-mass. Although the system is an infinite-dimensional, we can explain many of our results in terms of a one degree-of-freedom system corresponding to a forced pendulum. Indeed, using the vorticity measured via particle imaging velocimetry allows us to make the model quantitative, and a comparison with our experimental results shows we can capture the basic phenomenology of this system.
Highlights
A systematic study of the simple pendulum commenced with the observations by Galileo and others, heralding their employment as timekeepers.[1]
Our pendulum consists of a thin fiber with a bending stiffness B0, linear mass density λ, length l, and mass Ms = λl glued at one end to a stiff polymer ring and introduced at the other end into the film at a point P using a pippete that does not penetrate the soap film and does not have a wake
The pivot P was located 0.5 m downstream from the nozzle to allow for the soap solution to reach a steady state with an average velocity V = 0.4–1.5 m/s
Summary
A systematic study of the simple pendulum commenced with the observations by Galileo and others, heralding their employment as timekeepers.[1]. In the presence of a ring, three new effects arise—gravity which stabilizes the pendulum, tension in the string induced by fluid drag which stabilizes the pendulum, and low frequency vortex shedding from the ring that can destabilize the pendulum, unlike what typically happens in a flag.
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