A pendulum in a flowing soap film
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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.