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i've been meaning to make a simulation of this to figure it out .. in short (1) there must have been some original tangential momentum in the swing and (2) the moment of inertia changing will effect the oscillation period
also it looks like there's a lot of energy being dissipated by friction/wind resistance
There's no reason that the changing moment of inertia should affect the amplitude or direction .. so it seems that the entire pattern is made by air resistance and friction
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