A uniform plate of mass M stays horizontally and symmetrically on two wheels rotating in opposite directions (figure 12-E16). The separation between the wheels is L. The friction coefficient between each wheel and the plate is t. Find the time period of oscillation of the plate if it is slightly displaced along its length and released.

A uniform plate of mass M stays horizontally and symmetrically on two wheels rotating in opposite directions (figure 12-E16). The separation between the wheels is L. The friction coefficient between each wheel and the plate is t. Find the time period of oscillation of the plate if it is slightly displaced along its length and released.

Let x be the displacement of the plank towards left. Now the center of gravity is also displaced through x, in displaced position,

Taking moment about G, we get

Now,

Similarly,

Since,

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