Two light identical springs of spring constant \( k \) are attached...

Two light identical springs of spring constant \( k \) are attached horizontally at the two ends of an uniform horizontal rod \( A B \) of length \( / \) and mass \( m \). The rod is pivoted at its centre ' \( O \) ' and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure.

The rod is gently pushed through a small angle and released.
The frequency of resulting oscillation is (2019 Main, 12 Jan I)
\begin{tabular}{ll} \( = \) & (a) \( \frac{1}{2 \pi} \sqrt{\frac{2 k}{m}} \) \\ \hline & (c) \( \frac{1}{2 \pi} \sqrt{\frac{6 k}{m}} \) \end{tabular}
(b) \( \frac{1}{2 \pi} \sqrt{\frac{3 k}{m}} \) (d) \( \frac{1}{2 \pi} \sqrt{\frac{k}{m}} \)
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