Suppose that when a certain skyscraper is disturbed from rest, its top sways bac

Question

Suppose that when a certain skyscraper is disturbed from rest, its top sways back and forth in such a way that its maximum deflection from the vertical axis of the building to either side is always 98% of its previous maximum deflection on the other side of that axis, which always occurs 8 seconds earlier. After a strong wind gust, assume that the top of the building is 2 feet from that vertical axis. How many times will the top of the building cross the vertical axis before the amplitude of the oscillation falls below 3 inches? How long will it take for this to happen? (Give the answer in minute)

Explanation / Answer

1) let the required number be n

0.98^n * 2 feet < 3 inch

0.98^n *2*12 < 3

0.98^n < 1/8

0.98^n < 0.125

n > 102.929

n = 103

2) time = 103*8 sec

= 824 sec

= 13 min 44 sec

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