Question

Jami is trying to model the movement of a tire. In order to properly model the movement, she is going to focus on the movement of the tire's air nozzle. The nozzle is on the right side of the tire and she is going to treat that position as the equilibrium position. She then slowly rotates the tire so that the nozzle goes up at the beginning of the rotation, and follows its change in height.
The distance of the nozzle from the center of rotation is nine inches. She finds that it takes eight seconds for the tire to make a single revolution.




Which of the following functions best models the position of the nozzle?




A. s(t)=9sin(4pi t)



B.s(t)=9sin(pi/4 t)



C.s(t)=9cos(4pi t)



D. s(t)=9cos(pi/4 t)

Answer 1

From the given data it is clear that the amplitude of the wave will be 9 inches.

It is also clear that the speed of rotation, ω, will be: $\omega=\frac{2\pi}{T}=\frac{2\pi}{8}=\frac{\pi}{4}$

Now, it is given that the nozzle is on the right side of the tire and that position is going to be treated as the equilibrium position, the tire is then rotated such that the nozzle goes up at the beginning of the rotation. This condition is possible only when we have a Sine (Sin) function.

Thus, our final answer can be arrived as:

$Amplitude\times Sin(\omega t)$

$9\times sin(\frac{\pi}{4}t) =9sin(\frac{\pi}{4}t)$

Thus, out of the given options, option B is the correct answer.