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 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

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Aicharya · Accepted Answer

$ \begin{aligned} & 	ext { Restoring torque }=-(2 k x) \cdot \frac{L}{2} \ & \qquad \alpha=-\frac{k L(L / 2 	heta)}{I}=-\left[\frac{k L^2 / 2}{M L^2 / 12}ight] \cdot 	heta \end{aligned} $ $ \begin{aligned} & =-\left(\frac{6 k}{M}ight) 	heta \ 	herefore \quad f & =\frac{1}{2 \pi} \sqrt{\left|\frac{\alpha}{	heta}ight|}=\frac{1}{2 \pi} \sqrt{\frac{6 k}{M}} \end{aligned} $

A uniform rod of length $L$ and mass $M$ is pivoted at the centre. Its two ends are attached to two springs…

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