Harmonic motion of coupled pendula

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Homework Help Overview

The discussion revolves around the dynamics of coupled pendula, specifically exploring their periods, amplitudes, and the potential for chaotic motion. The original poster expresses curiosity about the mathematical treatment of this system, which is not a traditional homework problem but relates to concepts in harmonic motion and oscillations.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the possibility of finding the period and amplitude of coupled pendula, with some questioning the conditions under which chaotic motion may arise. References to external resources and theories, such as normal modes, are mentioned as potential avenues for further exploration.

Discussion Status

The conversation is ongoing, with participants sharing resources and theories related to the behavior of coupled pendula. There is an acknowledgment of the complexity of the system and the conditions that may lead to different types of motion, including chaotic and ergodic behavior.

Contextual Notes

The original poster notes a lack of comprehensive mathematical resources on the subject, indicating that much of the available information is focused on demonstrations rather than theoretical analysis.

bigevil
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This isn't a homework problem specifically, but I was wondering if it is possible to find the period, amplitude, etc of a slightly more complex system.

I found one on this page (http://www.physics.ucla.edu/demoweb...e_harmonic_motion/simple_harmonic_motion.html) and it's called a coupled pendulum, where two pendulums are connected by a spring and then oscillated.

I've heard that coupled pendula can cause chaotic motion under certain conditions, but I've seen such a system appear in a local exam (equivalent to pre-university or A Levels, in the UK), so I think it's not undoable. But I haven't found much about the mathematics of these systems, though, everything Google turns out are lab demos.
 
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Look up the theory of normal modes.
 
Chaotic motion may occur only if the coupling is strong and nonlinear.
Otherwise it may be ergodic, but this is not as funny as chaotic.
Coupling and uncoupling, this is most part of the job in physics.
 

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