Discussion
A structure of period 1.0 s completes how many cycles of free vibration in ten seconds, damping being neglected?
Answer: C
Correct answer: 10
The number of cycles is the elapsed time divided by the period:
\[ \frac{10}{1.0} = 10 \]
The period is the time for one complete cycle, so this is a matter of definition rather than of dynamics. It is worth noting how slow that is: a one-second building sways at 1 Hz, which is visible and perceptible to occupants, and is why serviceability under wind is checked for tall buildings as well as strength under earthquake.
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