Tuned mass damper · floors 87–92 · 660 tonnes
Two identical towers face the same wind. The one on the right has the golden pendulum hanging near its top; the one on the left has it locked. Change the wind and watch how the ball swings against the building to calm it down.
The damper removes roughly the same share of sway at every wind speed, because doubling the wind doubles every push and the tower's reply alike. The bump near 50 m/s is resonance lock-in: the wind's swirls arrive every 6.8 s, the tower's own rhythm, and that is exactly what the pendulum is tuned for. A measurement over a few minutes wanders well above and below this line, because the tower completes only about nine swings a minute and random gusts dominate so few swings. The curve leaves out the stopper ring, which only comes into play in the most extreme winds.
As wind flows past the tower it peels off in alternating swirls, left then right, called vortex shedding. Each swirl gives the tower a sideways nudge. The faster the wind, the faster the nudges come.
Like a tuning fork, Taipei 101 prefers to sway back and forth once every 6.8 seconds or so. When the gusts or swirls line up with that beat, each push adds to the last and the sway grows. That is resonance. Try the “Resonance lock-in” preset.
The ball hangs on cables tuned to the same 6.8 s period. When the building leans one way, the ball lags behind and ends up swinging in the opposite direction, so its weight pulls the tower back toward center.
Eight hydraulic cylinders connect the ball to the floor. Every swing forces oil through small valves, turning the tower's motion into a little heat. Energy that leaves through the pistons is energy the tower no longer sways with.
The spire has two small dampers of its own (sources give 4.5 or 6 t each), which this model leaves out. Taipei 101 stopped publishing damper movement data in 2021.
About the model: each tower is simplified to a single swaying mass (first mode, 6.8 s period, 1.2% structural damping, 120,000 t effective mass) with the 660 t pendulum attached to one of them. Wind force combines random gusts with vortex shedding at a Strouhal number of 0.14 on a 48 m wide tower. The numbers show how a tuned mass damper behaves; they are not engineering data for the real building.