A classical mechanics problem by Rishabh Deep Singh

Classical Mechanics Level pending

Two wheels which are rotated by some external source with constant angular velocity (\(\omega = \pi \text{ units}\)) in opposite directions as shown in the figure above. A uniform plank of mass \(M = 1\text{ units}\) is placed symmetrically. The friction coefficient between each wheel and the plank is \(\mu = 1\text{ units}\). Find the frequency of oscillation, when the plank is slightly displaced along its length (\(L=1 \text{ units}\)) and relapsed.

Details and Assumptions:

  • \(g = \pi^2 \text{ units} \).

  • Neglect end effect caused by extra length of plank.


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