The New England Merchants Bank Building in Boston is 152 m high. On windy days it sways with a frequency of 0.18 Hz , and the acceleration of the top of the building can reach 1.9 % of the free-fall acceleration, enough to cause discomfort for occupants. Required:
What is the total distance, side to side, that the top of the building moves during such an oscillation?

The total distance, side to side, that the top of the building moves during such an oscillation is approximately 0.291 meters.

Explanation:

Let suppose that the building is experimenting a Simple Harmonic Motion due to the action of wind. First, we determine the angular frequency of the system (), in radians per second:

(1)

Where is the frequency, in hertz.

If we know that , then the angular frequency of the system is:

The maximum acceleration experimented by the system is represented by the following formula, of which we estimate amplitude of the oscillation:

(2)

Where:

- Ratio of real acceleration to free-fall acceleration, no unit.

- Free-fall acceleration, in meters per square second.

- Amplitude, in meters.

If we know that , and , then the amplitude of the oscillation is:

The total distance, side to side, is twice the amplitude, that is to say, a value of approximately 0.291 meters.