# Simple Harmonic Motion...10

Discussion in 'Geometry and Trigonometry' started by nycmathguy, Mar 2, 2022.

1. ### nycmathguy

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Can you show me how to graph SHM functions given an interval? How is this done using desmos? How is this done using Wolfram? How is this done using mathway.com?

Sample:

Graph s = 5 cos [(pi/4)(t)] where t is between 0 and 16.

Thank you. Sleep time.

nycmathguy, Mar 2, 2022
2. ### MathLover1

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MathLover1, Mar 2, 2022
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3. ### nycmathguy

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Thank you for the graph. Can you help me answer the following 4 questions using the graph?

1. Determine the times in this interval at which the mass is farthest from the origin.

2. When during the interval of time [0, 16] does the mass pass through the origin?

3. When during the interval of time [0, 16] does the mass move to the right? In other words, when does s increase?

4. When during the interval of time [0, 16] does the mass move left? In other words, when does s decrease?

Thank you very much.

nycmathguy, Mar 3, 2022
4. ### MathLover1

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s = 5 cos [(pi/4)(t)] t is between 0 and 16

1. Determine the times in this interval at which the mass is farthest from the origin.

given: t is between 0 and 16

so, t=16

2. When during the interval of time [0, 16] does the mass pass through the origin?

no (cosine starts at (0,5) )

3. When during the interval of time [0, 16] does the mass move to the right? In other words, when does s increase?
yes, it moves to the right

Absolute Maximum: (0,5),(8,5),(16,5)
Absolute Minimum: (4,-5),(12,-5)
increase from min to max point: from (4,-5) to (8,5) and from (12,-5) to (16,5)

4. When during the interval of time [0, 16] does the mass move left? In other words, when does s decrease?
it does not move left

decreases: from (0,5) to (4,-5) and from (8,5) to (12,-5)

MathLover1, Mar 3, 2022
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5. ### nycmathguy

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nycmathguy, Mar 3, 2022
6. ### Country Boy

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I believe Math1 is interpreting the questions incorrectly.
"1. Determine the times in this interval at which the mass is farthest from the origin.

2. When during the interval of time [0, 16] does the mass pass through the origin?"

Math1 is interpreting this as asking when a point on the graph is farthest from the origin (at the far end of the graph, t= 16) and when the graph passes through the origin (it never does). But the question asks about the mass, not the graph. I interpret this graph as showing a mass moving back and forth equal distances on either side of the center point, its "origin". The mass is at greatest distance from this origin (not the origin of the graph) when t= 0, 4, 8, 12, and 16. The mass is passing through the origin when t= 2, 6, 10, and 14.

Last edited: Mar 4, 2022
Country Boy, Mar 4, 2022
7. ### MathLover1

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right, I choose t=16 only because he knows max is repeated and I was expecting him to say that

MathLover1, Mar 4, 2022
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