A researcher observes and records the height of a weight moving up and down on the end of a spring. At the beginning of the observation the weight was at its highest point. From its resting position, it takes 12 seconds for the weight to reach its highest position, fall to its lowest position, and return to its resting position. The difference between the lowest and the highest points is 10 in. Assume the resting position is at y = 0.
Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.
We have the form
y = Asin (Bx)
The amplitude, A, is [ difference between highest and lowest points ] / 2 = 10/2 = 5
The period is 12 sec
B = 2pi / period = 2pi/ 12 = pi/6
So.....the equation of the function is
y = 5sin [ ( pi / 6) x ]
Here's the graph : https://www.desmos.com/calculator/6ejfoskflu