Graphs relating to simple harmonic motion

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SUMMARY

The discussion centers on identifying the correct graph representation of velocity in simple harmonic motion, specifically focusing on the answer being 5. Participants analyze the characteristics of velocity at maximum and minimum displacement, noting that velocity equals zero at these points. The conversation highlights the importance of understanding variable spring forces and the non-linear nature of acceleration, ultimately leading to the conclusion that option D is incorrect due to its representation of constant acceleration, which does not apply in this context.

PREREQUISITES
  • Understanding of simple harmonic motion principles
  • Knowledge of conservation of energy in mechanical systems
  • Familiarity with graph interpretation in physics
  • Basic concepts of variable spring forces and their effects on motion
NEXT STEPS
  • Study the equations of motion for simple harmonic oscillators
  • Learn about the relationship between potential energy and kinetic energy in oscillatory systems
  • Explore graphical representations of velocity and acceleration in harmonic motion
  • Investigate the effects of variable forces on oscillatory motion
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to clarify concepts related to simple harmonic motion and graph interpretation.

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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