Consider small-amplitude oscillations of a rocking horse. Movement occurs only in the vertical plane, The base semi- circular has radius R. When the horse is at rest its center of gravity is at a height d from the ground. The total mass is M and the moment of inertia about its center of mass is I = Mrg2  (rg is the radius of gyration). Assume that the base rolls without slipping on the floor and that d < R. Neglect damping. (a) Use your intuition and dimensional analysis to estimate an expression for the natural frequency ω0 of small oscillations

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