Final answer:
It is false that increasing a building's mass decreases its fundamental period of vibration; the period actually increases with mass for a simple mass-spring system, and for buildings, it is also influenced by structural stiffness and mass distribution.
Step-by-step explanation:
The statement that increasing a building's mass decreases its fundamental period of vibration is false. In fact, for a simple mass-spring system, the period of vibration is directly proportional to the square root of the mass. When factors like a building's height and construction are considered, the period of vibration, or natural frequency, is also influenced by the stiffness of the structure and its mass distribution. Tuned-mass dampers, like the one in the Comcast Building with its 300,000-gallon water tank, are designed to counteract oscillations by moving out of phase with the building at the same natural frequency, hence reducing sway and vibrations due to winds or seismic activity.