Final answer:
The heavy mass in a tuned-mass damper system installed in tall buildings oscillates 180° out of phase with the swaying building to mitigate oscillations and prevent structural damage. Option C is the correct answer.
Step-by-step explanation:
Very tall buildings often incorporate damping systems to reduce resonance and the risk of structural damage due to wind or seismic activity. These systems, commonly known as tuned-mass dampers or harmonic absorbers, consist of a mass that is free to oscillate horizontally, connected by springs and shock absorbers to the building's structure. The purpose of these dampers is to counteract the oscillations of the building through a principle known as resonance control.
When a building sways due to external forces like wind or an earthquake, the damper is designed to move out of phase with the building's oscillation. This means that as the building moves in one direction, the mass moves in the opposite direction, effectively reducing the amplitude of the building's oscillation.
The key to this process lies in the frequency of oscillation, where the mass of the damper is tuned to move at the same frequency but in the opposite phase as the building's swaying, causing what is known as destructive interference. This helps mitigate the sway and prevent resonance, which could amplify the oscillations and possibly lead to structural failure.
The correct answer to the question of how the heavy mass will move in relation to the swaying building is C. The heavy mass will oscillate 180° out of phase with the swaying building, which effectively reduces the building's motion.