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

Answer:

The graph is attached below :

Step-by-step explanation :

For better understanding of the solution, see the graph which is attached below :

The first point will be at the max height not on the mid line.

Now, using the concept of sine tool, the function can be found to be :

y  =  A·sin(B·x - C) + D

where, Amplitude =  A = 10    

Period  =  12 seconds

$B=\frac{2\cdot \pi}{period}\\\\\implies B=\frac{2\cdot \pi}{12}\\\\\implies B=\frac{\pi}{6}$

Since at x  = 0, the weight is at its highest point

Therefore, At x = 0 the sine graph is shifted back by $\frac{\pi}{2}$ units. Thus,

$C= -\frac{\pi}{2}$

The mid line of the graph is  y  = 0

⇒ D = 0

Hence, The function  is  :

$\bf y=10\cdot \sin((\frac{\pi}{6})\cdot x+\frac{\pi}{2})$