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## Homework Statement

kleppner 8.3.

a pendulum is at rest with its bob pointing toward the center of the earth.

the support of the pendulum iw moved horizontally with uniform acceleration a, and the pendulum starts to swing. Neglect rotation of earth. Consider the motion of the pendulum as the pivot moves over a small distance d subtending angle theta=d/R<<<1 at the center of the earth, R is Earth radius. Show that if period of pendulum is 2pi/w, w=root(g/R), then the pendulum will continue to point toward the center of the Earth if effects of order (theta)^2 and higher are neglected.

## Homework Equations

I am not sure other than torque eaquation. relevant equations in chapter seven here pg 318-323. Here is the question printed in the book.

http://books.google.com/books?id=Hm...rough a point on the rim of the hoop"&f=false

## The Attempt at a Solution

I believe it has something to do with the pendulum being in equilibrium in the accelerating axis, with gravity and the fictitious force due to acceleration acting on it. But I don't know how to implement the other elements of the question, like distance d, angle theta, or w.

And if the pendulum always faces center of earth, then gravity doesn't exert torque on pendulum in acceleration frame, so no equilibrium equation between the torque from gravity and the fictitious force's torque makes sense.

Please help.

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