All Problems

Mechanical Oscillations

Problem 4.61

A mock-up of a CO 2_{2} molecule consists of three balls interconnected by identical light springs and placed along a straight line in the state of equilibrium. Such a system can freely perform oscillations of two types, as shown by the arrows in Fig. 4.20.4.20 . Knowing the masses of the atoms, find the ratio of frequencies of these oscillations.

Reveal Answer
ω2/ω1=1+2m0/mC≈1.9, where m0 and mC are the masses of oxygen and carbon atoms.\omega_{2} / \omega_{1}=\sqrt{1+2 m_{0} / m_{\mathrm{C}}} \approx 1.9, \text { where } m_{0} \text { and } m_{\mathrm{C}} \text { are the masses of oxygen and carbon atoms.}
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