A uniform rod of length $L$ and mass $M$ is pivoted at the centre. Its two ends are attached to two springs of equal spring constants $k$. The springs are fixed to rigid supports as shown in the figure, and the rod is free to oscillate in the horizontal plane. The rod is gently pushed through a small angle $\theta$ in one direction and released. The frequency of oscillation is
A uniform rod of length $L$ and mass $M$ is pivoted at the centre. Its two ends are attached to two springs of equal spring constants $k$. The springs are fixed to rigid supports as shown in the figure, and the rod is free to oscillate in the horizontal plane. The rod is gently pushed through a small angle $\theta$ in one direction and released. The frequency of oscillation is
- [IIT 2009]
- A
$\frac{1}{2 \pi} \sqrt{\frac{2 k}{M}}$
- B
$\frac{1}{2 \pi} \sqrt{\frac{k}{M}}$
- C
$\frac{1}{2 \pi} \sqrt{\frac{6 k}{M}}$
- D
$\frac{1}{2 \pi} \sqrt{\frac{24 k}{M}}$
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