A nice simple harmonic oscillator

Two parallel cylinders spin in opposite directions as shown. The distance between the center of the cylinders is \(a=1\) m . A straight uniform bar of length \(L>a\) rests on the cylinders. The coefficient of kinetic friction between the bar and a cylinder is \(\mu=0.1\). Find the period of the oscillations that result from displacing the bar from its equilibrium position, in seconds.

Use \(g=10\) m/s\(^2\).

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