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R.Fizpatricks' problem from his online "Lectures on CM"

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In those "Lectures on classical mechanics" in problem 2.4. for 'Newtonian mechanics' section the author gets the expression for angular frequency of small oscialations as the square root from the ratio of potential energy and moment of inertia in equilibrium, based on the virial theorem formula, presented in the text of the problem. Now, the latter formula I have easily proven, but could not figure out how he gets the angular frequency expression mentioned above from it.
Any takers? Thanks in advance.

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