A thin rod of length (L) and area of cross - section (S) is pivoted at its lowest point (P) inside a stationary, homegeneous and non - viscous liquid. The rod is free to ratate in a vertical plane about a horizontal axis passing through (P). The density (d_1) of the material of the rod is smaller than the density (d_2) of the liquid. The rod is displaced by a small angle (theta) from its equilibrium position and then released. Show that the motion of the rod is simple harmonic and determine its angular frequency in terms of the given parameters.
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Answer

`[omega = [(3(d_(2)-d_(1))g)/(2d_(1)L)]^(1//2)]`