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Write down the equations of motion for free oscillations of the system of mechanical oscillators. Show...

Write down the equations of motion for free oscillations of the system of mechanical oscillators. Show that assuming simple harmonic solutions leads to the normal-mode frequencies given by equations (1), (2) and (3). (Coupled Oscillators)

ω^2 = (2 − √ 2)k/m (1)

ω^2 = 2k/m (2)

ω^2 = (2 + √ 2)k/m (3)

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