Graphs relating to simple harmonic motion

AI Thread Summary
The discussion focuses on identifying the correct graph related to simple harmonic motion, with participants debating the validity of different options. One user initially selected option D but later considers option 5 to be correct, prompting requests for clarification on the reasoning behind this choice. Key points include the understanding that velocity is zero at the maximum and minimum displacements, which influences the graph's shape. The conversation highlights the importance of recognizing the relationship between velocity and position using conservation of energy principles. Ultimately, the discussion emphasizes the need to accurately interpret the graphical representation of motion in harmonic systems.
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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