In assume that the differential equation of a simple pendulum of length L isLθ" + gθ = 0, where g = GM/R2 is the gravitational acceleration at the location of the pendulum (at distance R from the center of the earth; M denotes the mass of the earth).
A certain pendulum keeps perfect time in Paris, where the radius of the earth is R = 3956 (mi). But this clock loses 2 min 40 s per day at a location on the equator. Use the result of Problem 5 to find the amount of the equatorial bulge of the earth.
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