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Coupling, according to wiki, is the condition of two systems when they interact with each other.

Now, I came across the terms harmonic oscillator and coupled oscillators. Now,what is the difference between the two? I read the wiki article of oscillation; but in vain. They only wrote that the later has higher degrees of freedom. What is meant by that?

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Consider the case that you have two oscillators (harmonic or otherwise). It is the case that either

  1. The oscillators are independent, i.e., non-interacting
  2. The oscillators are coupled, i.e., interacting

If (1), the differential equations for the system are just two single oscillator equations, e.g., the acceleration of one mass does not depend on the position of the other mass.

If (2), the differential equations are 'mixed', e.g., the acceleration of either mass depends on the difference in the position of the masses.

The term harmonic oscillator is opposed to anharmonic oscillator.

The natural (unforced) oscillation of a harmonic oscillator is a sinusoid, i.e., has a single frequency.

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