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Undamped Coupled Oscillators

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Undamped coupled oscillators:

Two identical undamped oscillators, A and B, each of mass m and natural frequency ω_0 are coupled in such a way that the coupling force exerted on A is σm(d^2x_b/dt^2), and the coupling force exerted on B is σm(d^2x_a/dt^2), where σ is a coupling constant of magnitude less than 1.

Find and describe the normal modes of the coupled system and the normal frequencies.

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