Harmonic motion of coupled pendula

AI Thread Summary
The discussion centers on the analysis of coupled pendula, specifically how to determine their period and amplitude in a more complex system where two pendulums are connected by a spring. It highlights that while coupled pendula can exhibit chaotic motion under certain conditions, they are also manageable for educational purposes, as seen in local exams. The conversation references resources for understanding the mathematics involved, particularly the theory of normal modes. It notes that chaotic behavior is more likely with strong, nonlinear coupling, while ergodic motion is less dynamic. Overall, the topic emphasizes the importance of coupling and uncoupling in the study of harmonic motion.
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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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