7. in physics lab, harper attaches a wireless sensor to one of the spokes of a bicycle wheel spinning freely…

7. in physics lab, harper attaches a wireless sensor to one of the spokes of a bicycle wheel spinning freely on its axle. the graph below shows the sensors height above the ground, in centimeters, over time t, measured in seconds. write an equation in terms of y, height in centimeters above the ground, and t, time in seconds, to represent the given context.

7. in physics lab, harper attaches a wireless sensor to one of the spokes of a bicycle wheel spinning freely on its axle. the graph below shows the sensors height above the ground, in centimeters, over time t, measured in seconds. write an equation in terms of y, height in centimeters above the ground, and t, time in seconds, to represent the given context.

Answer

Explanation:

Step1: Determine the amplitude

The amplitude (A) is half the distance between the maximum and minimum values. The maximum value (y_{max}=66) and the minimum value (y_{min} = 6). So, (A=\frac{y_{max}-y_{min}}{2}=\frac{66 - 6}{2}=30).

Step2: Determine the vertical shift

The vertical shift (D) is the mid - line of the function. (D=\frac{y_{max}+y_{min}}{2}=\frac{66 + 6}{2}=36).

Step3: Determine the period

The period (P) is the distance between two consecutive maximums (or minimums). Using the points ((6.25,66)) and ((15.25,66)), (P=15.25 - 6.25 = 9). Then, the frequency (B=\frac{2\pi}{P}=\frac{2\pi}{9}).

Step4: Determine the phase shift

We can use the cosine function (y = A\cos(B(t - C))+D). Let's assume (C = 0) (since we can start the analysis from a convenient point). Using the cosine function (the graph has a maximum - like point that we can relate to the cosine function's standard form).

Answer:

(y = 30\cos\left(\frac{2\pi}{9}t\right)+36)