Pendulum mechanics and coherence

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Discussion Overview

The discussion explores the relationship between the oscillation of a pendulum and the concepts of coherence and incoherence, particularly in the context of energy transformation between potential and kinetic forms. It touches on theoretical implications and statistical measures related to collections of pendulums and their micro-level behaviors.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants inquire whether the oscillation of a pendulum can be described in terms of coherence and incoherence, suggesting that these concepts may apply to the energy states of the pendulum.
  • One participant proposes that coherence could be viewed as a statistical measure of a collection of pendulums, rather than a single pendulum.
  • Another participant argues that at maximum potential energy, the molecular vibrations of the pendulum material could be more random and thus "incoherent," while at kinetic maximum, they might exhibit more coherence due to shared motion.
  • A question is raised regarding whether the entropy of a freely oscillating pendulum oscillates in magnitude, prompting further exploration of the relationship between coherence and entropy.
  • There is a discussion about entropy as a state function at thermodynamic equilibrium and its potential relationship with coherence in terms of micro-states available for energy storage.

Areas of Agreement / Disagreement

Participants express varying views on the applicability of coherence and entropy to pendulum mechanics, indicating that multiple competing perspectives remain without a clear consensus.

Contextual Notes

Participants acknowledge uncertainties regarding how entropy is measured in the dynamic behavior of a pendulum and the implications of coherence on micro-states.

BaghdadSerai
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Is there an established context in which the oscillation of a pendulum between potential and kinetic forms of energy can be described in term of coherence, that is, viewed as an oscillation between coherence and incoherence? (here incoherence is taken as the antonym of coherence)
 
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Not a single pendulum, but a collection of pendulums (harmonic oscillators). Coherence is a statistical measure of a system.
 
I don't want to force one notion upon another, but it seems one could make a case for this view. At maximum potential the molecular vibrations of the pendulum material would be statistically more random, "incoherent"; at kinetic maximum they would share a single vector of motion, statistically be more "coherent". In addition, the material of the supporting rod, at the micro level, would cycle between an unconstrained random motion at the point of maximum potential and transition into a state of mitigating shared stress (perhaps a form of coherence) at kinetic maximum.
Thanks for your reply.
 
By your reasoning, the entropy of a freely oscillating pendulum will also oscillate in magnitude. Is that permissible?
 
Oh, entropy! Good question. I know entropy to be a state function at thermodynamic equilibrium, wherein the energy is evenly dispersed among the various micro-states of the system. I believe there would be a relationship between coherence within a system and the number of micro-states that could serve as storage modes for energy. I am uncertain as to how it is entropy is measured in pendulum's dynamic.
Again, thanks.
 

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