+0

# 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

+1
2156
2

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.

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.

At an ocean depth of 10 m, a buoy bobs up and then down 6 m from the ocean's depth. Ten seconds pass from when the buoy is at its highest point to when it's at its lowest point. Assume at x = 0 the buoy is at normal ocean depth.

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.

Thanks.

Feb 9, 2018

#1
+101252
+1

First one  [ the first point will be at the max height......not on the midline ]

y  =  Asin(Bx - C) + D

Amplitude  = 10   =  A

Period  =  8sec

B  =   2pi / period  =  2pi / 8  =   pi/ 4

Since at x  = 0, the weight is at its highest point  at x = 0....the sine graph is shifted back by pi/2 units....thus, C  = pi/2

D  = 0   ....(  the midline  is  y  = 0  )

The function  is

y  = 10sin ( (pi/4) x  + pi/4 )

Here's the graph  : https://www.desmos.com/calculator/dkcasvrnen

Feb 9, 2018
#2
+101252
+1

Second one

y  = Asin (Bx)  + C

Amplitude   =   6  = A

The period must be  2 * 10  =   20 sec

B  =  2pi/ 20    =   pi / 10

The midline is  y  = -10

So.....the function is

y  = 6sin ( (pi / 10) x )  -  10

Here's the graph of the function : https://www.desmos.com/calculator/ddtgqzriou

Feb 9, 2018