Graphs relating to simple harmonic motion

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Homework Help Overview

The discussion revolves around identifying the correct graph related to simple harmonic motion, specifically focusing on the relationship between position and velocity. Participants are analyzing their choices and reasoning regarding which graph accurately represents the motion described.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants are sharing their reasoning for selecting specific graphs, questioning the validity of their choices, and discussing the characteristics of velocity in simple harmonic motion. There is an exploration of the implications of velocity being zero at maximum and minimum positions, as well as considerations of how velocity behaves with variable acceleration.

Discussion Status

The discussion is active, with participants providing insights and questioning each other's reasoning. Some guidance has been offered regarding the relationship between velocity and position through energy conservation principles, but no consensus has been reached on the correct graph.

Contextual Notes

Participants are encouraged to avoid posting direct answers to the problem until certain members have had a chance to contribute, indicating a collaborative approach to problem-solving. There is also mention of homework constraints regarding the nature of the discussion.

RoboNerd
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Homework Statement



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Homework Equations


None.

The Attempt at a Solution


Hi everyone. Apparently 5 is the right answer, although I chose D.

Could anyone please weigh in with their thoughts about why 5 is right and my answer is apparently wrong?

Thanks!
 
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Please explain how you got your answer.
 
Velocity can also be negative...
 
Physics-Tutor said:
Velocity can also be negative...
True, but that does not rule out any of the graphs. There is no claim that the graph represents an entire cycle. There is a better reason for choosing 5. What would the graph of velocity actually look like?

Edit: please do not post an answer to that on this thread, at least not until RoboNerd has had a chance to answer it.
 
Hi everyone, robonerd is back, of course.

I know that at xmin and max, the velocity [with kinetic energy] = 0 instantaneously. Thus, I narrow down to B and D.
However, I know that with a variable spring force giving a variable acceleration, I will not have the velocity changing in a linear manner [constant acceleration with constant slope], so I rule out B. D is thus a potential answer. Why is D wrong?
 
RoboNerd said:
Hi everyone, robonerd is back, of course.

I know that at xmin and max, the velocity [with kinetic energy] = 0 instantaneously. Thus, I narrow down to B and D.
However, I know that with a variable spring force giving a variable acceleration, I will not have the velocity changing in a linear manner [constant acceleration with constant slope], so I rule out B. D is thus a potential answer. Why is D wrong?
Can you write an equation relating velocity and x?
 
Yes. Using conservation of energy I have:

( 1 / 2 ) * k * A^2 = a constant value = (1 / 2) * m * v^2 + ( 1/ 2) * k * x^2
 
RoboNerd said:
Yes. Using conservation of energy I have:

( 1 / 2 ) * k * A^2 = a constant value = (1 / 2) * m * v^2 + ( 1/ 2) * k * x^2
Good. Can you recognise that form as a common shape? (Think of v as the y coordinate.)
 

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