Tall buildings are not rigid. In a strong wind a skyscraper leans, springs back, leans again, swaying like a very stiff, very slow tuning fork. Nobody is in danger, but people on the top floors can feel it, and some get seasick. Engineers could add more steel to stiffen the tower. Or they can do something stranger: hang a giant weight inside it and let the weight move the wrong way on purpose.
Every building has a natural rhythm, the time it takes to sway once if you nudge it and let go. Wind gusts that arrive in time with that rhythm are the dangerous ones, because each push adds to the last, like pushing a child on a swing at just the right moments.
A tuned mass damper is a heavy weight on springs, or hung on cables, built to swing at the same rhythm as the building. When the tower sways right, the weight lags behind, then swings left a moment later, just as the tower comes back. Its inertia tugs against the motion each time. The building's energy is handed to the weight, which dumps it as heat in its dampers.
Taipei 101 is 508 metres tall, in a region of typhoons and earthquakes. Between its 87th and 92nd floors hangs a steel pendulum of 660 tonnes, the largest tuned mass damper on record according to Guinness World Records. One report credits it with cutting the building's sway by up to 40 percent. Its biggest recorded swing was about a metre, during Typhoon Soudelor in August 2015. The ball moving that far is the system working: it is taking the motion so the tower and its occupants don't have to.
Both towers below are hit by the same wind. The left one has no damper. The right one carries a weight, drawn as the lime ball. Change its size, change how well it is tuned, and change the rhythm of the wind. (Damping and wind are exaggerated so you can see the effect within seconds.)
With the wind at the tower's own rhythm and the damper close to tuned, the right tower stays far calmer while the ball swings wildly. Drag the tuning slider away from 1 and the benefit melts. A damper that is too slow or too fast never gets into step with the building, so it just rides along as dead weight.
Slide the wind rhythm away from 1 and the plain tower calms down by itself: off-beat gusts don't build up. That is why the damper matters most at the one rhythm that does the damage. More mass helps too, but with diminishing returns, and a heavier weight must be hung, housed and paid for. Real towers tune their dampers carefully, then check them against measurements once the building is finished.
Stiffer steel raises the tower's natural rhythm and costs a lot of material, which adds weight and money. A damper adds one carefully placed mass near the top, where sway is largest, and attacks the problem directly. The trick is that you do not fight the motion with force from outside. You let a second object absorb it, and time it so that it always arrives out of step.