A classical mechanics problem by Rishabh Deep Singh

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

Details and Assumptions:

  • g=π2 unitsg = \pi^2 \text{ units} .

  • Neglect end effect caused by extra length of plank.

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