All Problems

Mechanical Oscillations

Problem 4.61

A mock-up of a CO \(_{2}\) 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. \(4.20 .\) 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.}
Prev
Next