Question 19.QE.1: The vibration of a building The Empire State Building sways ......
The vibration of a building
The Empire State Building sways back and forth in high wind at a vibration frequency of 0.125 Hz. What is its period of vibration?
Represent mathematically Since we know the vibration frequency, we can determine the period T = 1/f.
T=\frac{1}{f}=\frac{1}{0.125 \mathrm{~Hz}}=\frac{1}{0.125 \mathrm{vib} / \mathrm{s}}=8.0 \mathrm{~s} / \mathrm{vib}=8.0 \mathrm{~s}
The period is quite long! Observations of the tower show that the amplitude of vibration at the top of the
Solve and evaluate The period is
T=\frac{1}{f}=\frac{1}{0.125 \mathrm{~Hz}}=\frac{1}{0.125 \mathrm{vib} / \mathrm{s}}=8.0 \mathrm{~s} / \mathrm{vib}=8.0 \mathrm{~s}
building in a high wind is less than 4 cm. The long period of vibration and relatively small amplitude means this vibration is unlikely to damage the building or affect its occupants.
Try it yourself: You sit on a rocking chair. It takes 12 s to complete six rocks—all the way back and all the way forward again. Determine the period and the frequency of the rocking.
Answer: 2.0 s period and 0.5 \text { rocks } / \mathrm{s}=0.5 \mathrm{~s}^{-1}=0.5 \mathrm{~Hz} frequency.