Question

3. Strong winds can apply a significant enough force to tall skyscrapers to set them into a back-and-forth motion. The amplitudes of these motions are greater at the higher floors and barely observable for the lower floors. It is said that one can even observe the vibration motion of the Sears Tower in Chicago on a windy day. As 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.

Answer 1

Here, requency is nothing but the number of vibrations made by a vibrationg body in 1 sec.

There fore, for calculting the frequency , the folllowing method is used

In 60 seconds. , 8.6 vibrations are made by the Sears Tower

in 1second , how many vibrations the Sears Tower can make

$\Rightarrow$ 1/ 60 $\times$ 8.6

= 8.6 /60 = 0.143 vibrations / second

Therefore , the frequency of the Sears Tower n = 0.143 vibrations / second

The time period T = 1/n = 1/ frequency = 60/8.6 =6.97 seconds

Therefore , The time period of the Sears Tower T = 6.97 seconds