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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 8 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 20 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. the placment of the dots were wrong when i tried to answer this question, can anyone please tell me specifically on where to place the dots on which box and axis, and if  possible the way you answered it.

Feb 5, 2019

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We have the form

y = Asin (Bt + C) + D

A is the amplitude.......it is the difference between the highest and lowest point divided by 2  = 20/2 = 10

B is the period......we can find this as follows

B =  2pi/period......the period is 8 seconds.....so we have    2pi / 8  =  pi/4

C=  the phase  shift  ....since the first point is on the midline which is y = 0.....this is the normal starting point for the sine function....so.....there is no phase shift

D = shift up/down.......there is none since the first point is on the midline,  y = 0

Thus....the function is

y =  10 sin ( (pi/4) t)

Here is a graph :https://www.desmos.com/calculator/queeoexbii   th

Feb 5, 2019