Now what can cause such a thing? There are a few possibilities:
Vortex Shredding: Has caused buildings to collapse, its periodic low pressure areas at a particular point.
Aeroelastic flutter: Caused the collapse of a bridge, a consequence of the object having an aerodynamic shape is that it starts oscillating.
Crosswinds: two or more gusts intersecting at the exact location of the swing.
Mechanical resonance: Slight oscillations matches natural frequency of the system, causing it to sway.
I'm not an expert, and do not know much about this, just putting together a list of possible explanations.
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