Harmonic motion of coupled pendula

[bigevil]

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.

 

[bigevil]

Wait, I found something: http://www.nikhef.nl/~h73/kn1c/praktikum/phywe/LEP/Experim/1_3_25.pdf

 

[christianjb]

Look up the theory of normal modes.

 

[lalbatros]

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.