Relativistic Harmonic Oscillator

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Homework Help Overview

The discussion revolves around the behavior of a relativistic linear harmonic oscillator, specifically how its acceleration changes with respect to the distance from the equilibrium point in a laboratory reference frame.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to express the position, velocity, and acceleration of the oscillator using trigonometric functions. They seek hints or guidance on how to proceed further. Other participants inquire about the specific question and suggest the potential use of Lorentz transformation in the context of the problem.

Discussion Status

The discussion is in an exploratory phase, with participants seeking clarification and guidance on the problem. Some have suggested possible approaches, but there is no explicit consensus on the next steps or methods to be employed.

Contextual Notes

There is a lack of detailed information regarding the specific parameters of the oscillator and the conditions under which the problem is being analyzed. Participants are questioning the assumptions related to the relativistic effects involved.

Petar Mali
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Homework Statement



How does change acceleration of relativistic linear harmonic oscillator with distance of equilibrium point in laboratory reference system?



Homework Equations







The Attempt at a Solution



[tex]x=x_0sin(\omega t+\varphi)[/tex]

[tex]\upsilon=\omega x_0cos(\omega t+\varphi)[/tex]

[tex]a=-\omega^2 x_0sin(\omega t+\varphi)[/tex]

What now?

Just hint or help I need. Thanks!
 
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Any idea?
 


Not at all. What's your question?
 


Idea of solving this problem?

Do i need to use Lorentz transformation

[tex]x'=\frac{x-ut}{\sqrt{1-\beta^2}}[/tex]

where [tex]x'= x'_0sin(\omega t'+\varphi')[/tex]?
 

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