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A uniform horizontal plank is resting sy...

A uniform horizontal plank is resting symmetrically in a horizontal position on two cylindrical droms , which are apinning in in opposite direction about their horizontal axes with equal angular velocity . The distance between the axes with equal angular velocity. The distance between the axes is `2 L` and the coefficient of friction between the plank and cylender is `mu` . If the plank is displaced slightly from the equilibrium position along its length and released, show that it performs simple horizontal motion. Caculate also the time period of motion.

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To solve the problem step by step, we will analyze the situation of the plank resting on two cylindrical drums and derive the equations governing its motion. ### Step 1: Understand the Setup - We have a uniform horizontal plank resting symmetrically on two cylindrical drums. - The distance between the axes of the drums is \(2L\). - The drums are rotating in opposite directions with equal angular velocity. - The coefficient of friction between the plank and the cylinders is \(\mu\). ...
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