Time period from potential energy expression

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SUMMARY

The discussion focuses on the potential energy expression U = 5x² - 20x and its implications for force in simple harmonic motion (SHM). The derived force expression, F = -10x + 20, indicates that the mean position is not at x = 0, but rather at x = 2. This adjustment is crucial for understanding the behavior of the system, as it directly affects the force calculation in SHM, which typically follows the form F = -kx.

PREREQUISITES
  • Understanding of potential energy and force relationships in physics
  • Familiarity with calculus, specifically differentiation
  • Knowledge of simple harmonic motion (SHM) principles
  • Ability to interpret and manipulate algebraic expressions
NEXT STEPS
  • Study the derivation of force from potential energy in different contexts
  • Learn about the characteristics of simple harmonic motion and its equations
  • Explore the implications of shifting the mean position in harmonic systems
  • Investigate the role of the spring constant (k) in SHM dynamics
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Students studying physics, particularly those focusing on mechanics and harmonic motion, as well as educators seeking to clarify concepts related to potential energy and force in SHM.

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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