Aresearcher 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.

The graph of the motion of the weight created with a sine function

showing the first point on the midline and second at the next lowest point.

Steps to plot the graph:

Location of the weight at the beginning of the observation = The highest point

The time it takes the weight to complete a cycle, T = 12 seconds

The difference between the lowest and highest point = 10 in.

The assumed location of the resting position is y = 0

The general form of the sine function is y = A·sin(B·x  + C) + D

The period, T = = 12

Therefore;

A = The amplitude

D = The vertical shift = 0

The difference between the highest and lowest point = 2 × A

At x = 0, the function is at the highest point, therefore;

sin(B×0  + C) = 1

sin(C) = 1

Therefore

The function is therefore;

Please find attached the graph of the function plotted with MS Excel,

showing the first point on the midline with coordinates approximately (3,

0), and the second point at the point (6, -5).

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answer:

(-8,7)

explanation:

we know that  

f

(

−

3

)

=

7

therefore, if we wish to get the output as 7, in the function, we need to have our input to be -3.

looking at the function  

f

(

x

+

5

)

, what should the value of x be, such that the input in the function becomes 7?

we simply equate the terms,

x

+

5

=

−

3

x

=

−

8

thus, the point on the new function would be  

(

−

8

,

7

)