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d 9.3 Pendulum on moving pivot
A pendulum is at rest with its bob pointing toward the center of the Earth. The support of the pendulum is moved horizontally with uniform acceleration a , and the
pendulum starts to swing. Neglect rotation of the Earth.
Consider the motion of the pendulum as the pivot moves over a
small distance d subtending an angle θ 0
≈ d / R e
« 1 at the center
of the Earth. Show that if the period of the pendulum is 2π f R e / g ,
the pendulum will continue to point toward the center of the Earth, if effects of order θ 0 2 and higher are neglected. (One way to make
such a long-period pendulum would be to place the pivot point of a long rod close to its center of mass.)

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