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Example of oscillations Example : A thin rod of length L and area of cross-section S is pivoted at its lowest point P inside a stationary, homogeneous and non viscous liquid (fig.1). The rod is free to rotate in a vertical plane about a horizontal axis passing through P. The density d, of the material of the rod is smaller than the density d 2 of the liquid. The rod is displaced by a small angle θ 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.   Solution : When the rod is displaced slightly through an angle θ with the vertical Fig.2, the effective upward force acting at the middle point G of the rod is:                                F= upward thrust – weight of rod                   ...