“Would the Hancock ever, really, have fallen down? Nobody knows, but nobody was willing to take the risk.”
—Robert Campbell, in The Boston Globe, March 3, 1995
Why would a modern skyscraper in Boston’s posh Back Bay neighborhood fall down? And what does that have to do with harmonic motion? The answer is as simple as pushing a child on a swing. After all, not many grandmothers can lift a ten-year-old boy overhead. Instead, put the child into a swing and let grandma push him a few dozen times. Soon he flies as high as grandma can reach.
As with many things, timing is key. A child on a swing is a form of pendulum with a natural frequency of motion. Deliver an impulse at the system’s natural frequency, and soon you will have a lot of energy stored in the system’s back-and-forth motion, or oscillation. That is what grandma does for her grandson, and that is what the wind did to the John Hancock Tower in Boston when it was completed in 1976.
Push a skyscraper to one side, and it tends to flex.
Elastic forces then tend to straighten the building out.
But when the wind repeatedly pushed the Hancock Tower at its natural frequency (0.14 Hz, or once every 7 s), the building continued to wobble, making occupants seasick and threatening to age its support structure prematurely.
What was worse was that the building not only bent—it twisted, too.
The two motions of bending and twisting resonated with each other, storing a large amount of vibrational energy in the process.
The solution came in the form of two 300-ton boxes attached to the Hancock’s frame by springs and fluid-filled “shock absorbers.”
Occupying the tower’s 58th floor, the boxes float on oil; because of their inertia, they remain nearly motionless as the building dances around them.
If the Hancock lurches or twists, the springs and shocks push or pull it back into alignment.
The system is tuned to the building’s natural frequency and transforms vibrational energy into easily dissipated heat.
Similar tuned mass dampers now operate in dozens of structures. One, a 730-ton pendulum in Taiwan’s half-kilometer-tall Taipei 101, has become a popular tourist attraction.