# Oscillations of a tetra-atomic molecule

**Electricity and Magnetism**Level 5

Consider the following model of a tetra-atomic molecule: Four point-charges with charge \(q\) and mass \(m\) are connected by light rigid rods of length \(l\). Clearly, the molecule is in equilibrium when the charges form a square of side \(l\). 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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