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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The solution is in the attached file cosc.pdf
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