# Oscillations of a triatomic molecule

**Electricity and Magnetism**Level 5

Consider the following model of a triatomic molecule: Three point-charges with charge \(q\) and mass \(m\) are connected by massless rigid rods of length \(l\). Clearly, the molecule is in equilibrium when the charges are aligned. Since this equilibrium is stable, the molecule can oscillate as shown in the figure. If the parameters \(q\), \(m\), and \(l\) satisfy
\[ \frac{k q^{2}}{m l^{3}}=10^{4}~\mbox{s}^{-2} \quad \textrm{where} \quad k=\frac{1}{4\pi \epsilon_{0}},\]
find the period \(T\) **in seconds** of small oscillations.

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