Final answer:
This question pertains to the physics behind building oscillations due to external forces and the engineering methods used to mitigate these oscillations through damping systems such as mass dampers.
Step-by-step explanation:
The question is related to the physics of building oscillations and harmonic motion, which deals with how skyscrapers respond to external forces such as wind or seismic activity. The New England Merchants Bank Building in Boston, which sways with a frequency of 0.16 Hz and can experience accelerations at the top of 2.5% of the free-fall acceleration, exemplifies the need for damping mechanisms. Such buildings often employ devices like tuned-mass dampers or liquid-column mass dampers, as mentioned with the Comcast Building in Philadelphia and the Citigroup Center in New York City, to reduce these potentially uncomfortable oscillations.
Understanding the physics behind how these dampers work involves concepts from simple harmonic motion and engineering design. An example of such an application is the design of a pendulum to reduce the swaying of a skyscraper, requiring calculations of the appropriate length and mass distribution of the pendulum. Another aspect is calculating the force constants for springs in damping systems that must oscillate with a given period or determining the energy stored in such systems for a given displacement.