Magnitude of Displacement for Harmonic Oscillator

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SUMMARY

The discussion focuses on determining the magnitude of displacement in a harmonic oscillator when elastic potential energy (U) equals kinetic energy (K). The relevant equations are U = (1/2)kx² for potential energy and K = (1/2)mv² for kinetic energy. Participants confirm that setting U equal to K is the correct approach to solve for displacement (x) in terms of angular frequency (ω) and amplitude (A). Understanding the relationship between displacement and velocity as functions of time is also emphasized as crucial for solving the problem.

PREREQUISITES
  • Understanding of harmonic oscillators and their properties
  • Familiarity with the equations for potential and kinetic energy
  • Knowledge of angular frequency (ω) and amplitude (A)
  • Basic understanding of the relationship between displacement and velocity in oscillatory motion
NEXT STEPS
  • Study the relationship between displacement and velocity in harmonic motion
  • Learn how to derive the equations of motion for a harmonic oscillator
  • Explore the concept of energy conservation in oscillatory systems
  • Investigate the implications of varying amplitude (A) on displacement and energy
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators looking for insights into teaching harmonic oscillators and energy concepts.

Dortega120
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Homework Statement


A harmonic oscillator has angular frequency ω and amplitude A. What is the magnitude of the displacement when the elastic potential energy is equal to the kinetic energy? (Assume that U = 0 at equilibrium.)

Express your answer in terms of the variables ω and A.

Homework Equations



Potential Energy: U=(1/2)kx^2

Kinetic Energy: K= (1/2)mv^2

The Attempt at a Solution



Honestly, I don't really understand the question. What I was thinking had to be done at first was to set the PE formula equal to the KE formula, and then solve for x, which is the displacement.
 
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Dortega120 said:

Homework Statement


A harmonic oscillator has angular frequency ω and amplitude A. What is the magnitude of the displacement when the elastic potential energy is equal to the kinetic energy? (Assume that U = 0 at equilibrium.)

Express your answer in terms of the variables ω and A.

Homework Equations



Potential Energy: U=(1/2)kx^2

Kinetic Energy: K= (1/2)mv^2

The Attempt at a Solution



Honestly, I don't really understand the question. What I was thinking had to be done at first was to set the PE formula equal to the KE formula, and then solve for x, which is the displacement.
That is right, set PE equal to KE and solve for x, in terms of the data given: angular frequency ω and amplitude A. But you need to know how the displacement and the velocity are related. Both are function of time What are these functions?

ehild
 

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