The New England Merchants Bank Building in Boston is 152m high. On windy days it sways with a frequency of 0.19Hz , and the acceleration of the top of the building can reach 2.3% of the free-fall acceleration, enough to cause discomfort for occupants.
What is the total distance, side to side, that the top of the building moves during such an oscillation?

0.316 m.

Explanation:

Frequency, f = 0.19 Hz

Using curcular motion equation,

ω = 2π*f

= 1.19 rad/s

Maximum acceleration, a(max) = 2.3 % *9.8m/s^2

= 0.023 * 9.8

= 0.225 m/s^2

In simple harmomic motion,

a(max) = A*ω^2

Where,

A = amplitude

= 0.225/1.19^2

= 0.158 m

2A = 0.316 m.

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true tan speed = ang vel x radius