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# Question 1 and question 2

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If someone is willing to help me I would greatly appreciate it .

Question 1 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 20 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 6 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.

Question 2

At an ocean depth of 8 meters, a buoy bobs up and then down 5 meters from the ocean's depth. Sixteen seconds pass from the time the buoy is at its highest point to when it is at its lowest point. Assume at x = 0 the buoy is at normal ocean depth.

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.

Jan 14, 2019

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Period = 20 seconds (given)       Frequency = 1/period = 1/20

Starts at its highest point = cosine function

resting point = x axis (given)

Amplitude = 6/2 = 3   (1/2 of the height of the 'wave')

3 cos x    has  period of 2pi     to get period of 20   :    2pi/? = 20     then   ? = 2pi/20 =.1 pi

3 cos (1/10 * pi * x)

Sorry....I see Chris has pointed out that you may need to use the sine function....we will need to shift the curve 1/4 period to the left

20 sec * 1/4 = 5

3 sin (1/10 pi (x+5))

Jan 14, 2019
edited by ElectricPavlov  Jan 14, 2019
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Thanks, EP

Note Jenny :  If you have to use the sine function, here's a possibility :

Jan 14, 2019
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Here is a graph (with sin function) :    object starts at its highest position at t= 0     takes 20 sec for full cycle

Jan 14, 2019
edited by ElectricPavlov  Jan 14, 2019
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For the second one, the first sentence is a little confusing.....I'm assuming that  the amplitude is 5 meters...and the midline is 8 metrers below the water's surface....thus the highest point of the buoy is  3 meters below the surface of the water and the low point is  13 meters below the water's surface

Here's the graph : https://www.desmos.com/calculator/6umbpfydcn

Jan 14, 2019
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For some reason the graph is not showing with the link

jjennylove  Jan 15, 2019
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Try this, Jenny.....but I don't know....EP's interpretation may actually be correct.....!!!!

CPhill  Jan 15, 2019
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Number 2  (using sine function)

I think the amplitude is   up 5   and down 5 from the midline     Amplitude = 5   (Chris has a different interpretation)

5 sin ?x         period is 32 seconds     2pi/32 = 1/16 pi

5 sin( 1/16 pi x)      and it is shifted UP 8 meters

5 sin (1/16 pi x) + 8     SHould fit the bill !

Jan 15, 2019
edited by ElectricPavlov  Jan 15, 2019
edited by ElectricPavlov  Jan 15, 2019
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Here is a pretty picture !

Jan 15, 2019
edited by ElectricPavlov  Jan 15, 2019
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im quite unsure who is correct here.

Jan 15, 2019
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I cannot see Chris's graph , is it the same answer but different interperation as you had said ?

jjennylove  Jan 15, 2019
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Hmm im not sure myself . Both seem as if they could possibly work but there must be a word that differentes it to being the answer. I will try reading it over using both of yours explanations if you guys end up finding which one is correct could you guys let me know?

jjennylove  Jan 15, 2019
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Yah, the wording of the question is a bit unclear...and we both interpreted/read it differently....sorry for the confusion!

ElectricPavlov  Jan 15, 2019
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I read  :  Ocean depth 8     Up and down 5 from ocean depth (8)        which would mean it is bobbing up to 13   and down to 3....

ElectricPavlov  Jan 15, 2019
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would 8 meters be the midline ? since from 8 meters (0,8) the buoy bobs  up and down 5 from the midline?

jjennylove  Jan 15, 2019
edited by jjennylove  Jan 15, 2019
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yes,  8m is the midline (see the graph)

ElectricPavlov  Jan 15, 2019
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oh okay so the difference between your guys is whether the midline is posititve 8 or negatitive ? Hmmm okay .

What does the x=0 , could that possibly give a hint ?

jjennylove  Jan 15, 2019
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I'd go with EP's.....I think the buoy is floating on the water's surface......and the depth of the water = 8ft

So....the buoy would rise to a height of 13 ft  above the ocean bottom  and fall to a point 3 ft from the ocean's bottom

This makes more sense than mine.....

Jan 15, 2019
edited by CPhill  Jan 15, 2019
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That is what I am thinking it makes a bit more sense also just because it is a "buoy" , lets say if the ocean was 8 meters like how it says ( 8 meters depth" it wouldnt be able to go down any further since that is the "depth"( how far down it does) if that makese sense.

jjennylove  Jan 15, 2019
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Whew !   LOL          I think we solved all of the World's problems !

ElectricPavlov  Jan 15, 2019
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I think we did haha, thank you both for your help! i apprectiate it a lot

jjennylove  Jan 15, 2019
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Only the World's "buoy" problem......others  remain.....

Jan 15, 2019