Consider a pendulum suspended at some location on the earth, Physics

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Consider a pendulum suspended at some location on the earth

Consider a pendulum suspended at some location on the Earth. The length of the pendulum can be taken to be much shorter than the radius of the Earth. Approximate the Earth as a sphere. Find an equation for the angle, alpha, that the pendulum makes with the radial direction to the center of the Earth. Solve the equation assuming that alpha is small. At what theta is alpha maximum? What is the numerical value of the maximum alpha?

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Physics: Consider a pendulum suspended at some location on the earth

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