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.

Explanation:

The repetitive up and down motion of a weight (mass) in a spring depicts the simple harmonic motion.

The most basic equation for the simple harmonic motion around the rest position is:

Where A is the amplitude, T is the period, and t is the time.

The amplitude A is the vertical distance between the crest of the wave and the equilibrium (rest) position. It is half the maximum displacement of the mass.

The maximum displacement is the difference between the lowest and the highest points, which is 20 inches in the problem.

Hence, A = 20 / 2 = 10

The period, T, is the time for a complete cycle. This is the time for the weight to, starting from its resting position, reach its highest position, fall to its lowest position, and return to its resting position. This time is 8 seconds in the problem: T = 8.

Then you must graph the function:

Some points of that function that will permit you to draw the graph are when t = 0, t = 2, t = 4, t = 6, and t = 8

With that, you can sketch the function. Now, find attached the drawing using a graph calculator.

think about it deeply and passionately about this property

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