The Sears Tower vibrates back and forth, it makes about 8.6
vibrations in 60 seconds. Determine the frequency and the
period of vibration of the Sears Tower.

Frequency is 0.143 Hz; Period is 7 seconds

Explanation:

Number of vibrations = 8.6

Time required = 60 seconds

Period (T) = ?

Frequency of the vibrations (F) = ?

A) Recall that frequency is the number of vibrations that the Sears tower completes in one second.

i.e Frequency = (Number of vibrations / time taken)

F = 8.6/60 = 0.143Hz

B) Period, T is inversely proportional to frequency. i.e Period = 1/Frequency

T = 1/0.143Hz

T = 7 seconds

Thus, the frequency and period of the vibrations of the Sears Tower are 0.143 Hz

and 7 seconds respectively.