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 pendulum of length 100.10 in., located at a point at sea level where the radius of the earth is R = 3960 (mi), has the same period as does a pendulum of length 100.00 in. atop a nearby mountain. Use the result of Problem 5 to find the height of the mountain.
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