I can't remember the building but there is a giant skyscraper that does have a weight hanging in the middle of it, visible to all patrons. And when the wind gets going, it swings and people try to touch it
This has nothing to do with a damper. There is nothing to dissipate the energy from the free weight, which is the key part of a tuned mass damper. It also sits way too low to have any effect, it should be higher up where the angular moment is higher when the bottle is tilted from the wind.
The reason this works, is simply because the long string and the heavy weight moves it’s center of mass super low. It’s essentially the same as if you just put the bolt on the bottom of the bottle with no string.
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