Question

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A bicycle wheel is spinning in place. The vertical position of a point on the wheel, in inches, is described by the function f(t) = 13.5 sin (5 * 2πt) + 20. Time t is measured in seconds. What is the meaning of 13.5 in this context?

Answer 1

The 13.5 in this context is the amplitude of the sine function. It represents the maximum displacement of the point from its equilibrium position.

The function f(t) = 13.5 sin (5 * 2πt) + 20 describes the vertical position of a point on the wheel as a function of time. The sine function represents the cyclical motion of the point. The amplitude of the sine function is 13.5, which means that the point will move a maximum of 13.5 inches above or below its equilibrium position.

Explanation:

Answer 2

In the given context, the function f(t) = 13.5 sin(5 * 2πt) + 20 describes the vertical position of a point on the bicycle wheel, in inches, at any given time t in seconds.

The amplitude of the sine function, which is 13.5 in this case, determines the maximum displacement or distance of the point on the wheel from its equilibrium position (the midline).

In other words, the point on the wheel moves up and down by a maximum distance of 13.5 inches from the center of the wheel as it spins. This means that the diameter of the wheel is twice the amplitude, which is 27 inches.

So, 13.5 is the amplitude of the sine function and represents the maximum displacement of the point on the bicycle wheel from its equilibrium position.