Time period from potential energy expression

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Homework Help Overview

The discussion revolves around the potential energy expression U = 5x² - 20x and its implications for understanding the force acting on a particle. Participants are exploring the relationship between potential energy, force, and simple harmonic motion (SHM).

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the expression for force derived from the potential energy and question its alignment with the characteristics of SHM. There are inquiries about the nature of the force if the mean position is not at x = 0, leading to considerations of how the reference point affects the analysis.

Discussion Status

There is an ongoing exploration of the implications of the mean position on the force expression. Some participants have provided insights into how the force expression changes when the mean position is shifted, indicating a productive direction in the discussion.

Contextual Notes

Participants are considering the implications of having the mean position at x = 2 rather than at the origin, which raises questions about the assumptions underlying the problem setup.

Jahnavi
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Homework Statement


shm.jpg


Homework Equations

The Attempt at a Solution



U = 5x2 - 20x

F = -dU/dx

F = -10x + 20

The expression for force doesn't look like motion is SHM .

How should I deal with this ?
 

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Jahnavi said:

Homework Statement


View attachment 221130

Homework Equations

The Attempt at a Solution



U = 5x2 - 20x

F = -dU/dx

F = -10x + 20

The expression for force doesn't look like motion is SHM .

How should I deal with this ?
What should be the force if a particle performs SHM?
 
ehild said:
What should be the force if a particle performs SHM?

F = -kx

x is the displacement from the mean position .k is constant .
 
What happens if the mean position is not at x = 0?
 
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Chandra Prayaga said:
What happens if the mean position is not at x = 0?

OK . So the origin is not at the mean position .If it were then F=-kx .

But here mean position is at x= 2 .

Right ?
 
Right. I am sure you can now answer the original question.
 
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Chandra Prayaga said:
Right. I am sure you can now answer the original question.

Yes :smile:

Thanks !
 

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