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.(1) Use your intuition and dimensional analysis to estimate an expression for the natural frequency ω0 of small oscillations. Centro turning centerde giroCentrode masa center ofmassRd

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Answered: Consider small-amplitude oscillations…

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter6: Uniform Circular Motion And Gravitation

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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 = Mr_g² (r_g is the radius of gyration). Assume that the base rolls without slipping on the floor and that d < R. Neglect damping.

(1) Use your intuition and dimensional analysis to estimate an expression for the natural frequency ω₀ of small oscillations.

Centro turning center
de giro
Centro
de masa center of
mass
R
d

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