Small Oscillations about the equilibrium point:

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SUMMARY

The discussion focuses on finding the frequency of small oscillations around the equilibrium point for the potential function v(x) = (1/x^2) - (1/x). The equilibrium point is established at x=2 through differentiation. To determine the frequency, participants suggest using a Taylor series expansion around x=2, approximating the function to identify the dominant quadratic term, which characterizes the system as a simple harmonic oscillator.

PREREQUISITES
  • Understanding of potential energy functions in classical mechanics
  • Knowledge of differentiation and finding equilibrium points
  • Familiarity with Taylor series expansions
  • Concept of simple harmonic motion and its frequency calculation
NEXT STEPS
  • Study Taylor series expansion techniques for approximating functions
  • Learn about simple harmonic oscillators and their frequency derivation
  • Explore the application of differentiation in physics for equilibrium analysis
  • Investigate potential energy functions and their behavior near equilibrium points
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Students in physics, particularly those studying classical mechanics, as well as educators and anyone interested in understanding the dynamics of oscillatory systems.

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Homework Statement



v(x)= (1/x^2) -(1/x) Find the frequency of small osciallations about the equilibrium point

Homework Equations





The Attempt at a Solution


I have so far worked out the equilibrium point is at x=2, to get this i differentiated v(x) and solved it, but could anybody help me on how i could work out the frequency of small oscialltions for this problem?
 
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It's been a while, but I think I know what's next. You need to approximate the function around the point x=2. Do a taylor series and hopefully the higher order terms are much smaller than the quadratic term. From here you can call it a simple harmonic oscillator.
 

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