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5a) The gravitational force on a particle of mass m inside the earth at a distance...

5a) The gravitational force on a particle of mass m inside the earth at a distance r from the center (r < RE the radius of the Earth) is F = −mgr/R. Show that in an evacuated, frictionless tube, the particle would move back and forth through the tube with a simple harmonic motion and find the period of that motion.

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