Question

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.

Answer 1

To graph the function representing the height of the weight moving up and down on a spring, use the equation y = A sin(Bx + C) + D. In this case, the amplitude is 5 and the period is 12 seconds.

Step-by-step explanation:

To graph the function representing the height of the weight moving up and down on the spring, we can use the sine tool. The given information tells us that the weight takes 12 seconds to complete one cycle from its highest point to its lowest point and back to its resting position. The difference between the lowest and highest points is 10 inches. Since the resting position is at y = 0, the highest point will be at y = 5 inches and the lowest point will be at y = -5 inches.

To graph the function, we can use the equation for a general sine wave: y = A sin(Bx + C) + D, where A is the amplitude, B is the horizontal compression/stretch, C is the phase shift, and D is the vertical displacement. In this case, the amplitude is 5 inches, the horizontal compression/stretch is determined by the period of 12 seconds (B = 2π/period), the phase shift is 0 because the first point must be on the midline, and the vertical displacement is 0 because the resting position is at y = 0.

Therefore, the equation for the height of the weight as a function of time is y = 5 sin((2π/12)t).