Math CentralQuandaries & Queries


Question from San, a student:

During a strong wind, a tall builing, such as the CN Tower, can sway back and forth as much as 100cm, with a period of 10 seconds. Please help me to determine the equation for this function, in the form y=asinkx

Hello San.

The amplitude in the question is 50cm, assuming we interpret the question to mean there is 100cm difference between one extreme and the other (amplitude is measured from the center to either extreme). In the equation, the variable a is the amplitude.

If you let y be the variable representing the distance from the center line, then x could be considered the time component of the motion. It is left to determine the value of k, which clearly has some bearing on the period.

The sine function alone has a period of 2π, and in this question that takes 10 seconds. So

kx = 0 (at time x=0 seconds)
kx = 2π (at time x=10 seconds)
kx = 4π (at time x=20 seconds)
and so on.

Just pick x=10 and solve for k.

Hope this helps,
Stephen La Rocque.

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