The gravitational force inside a hollow Earth is zero.
But our Earth is not hollow. If the Earth were of uniform density, then the force would vary linearly inside the Earth. It is zero at the center -- just from symmetry -- and reaches the value at Earth's surface at Earth's surface! This linear force looks just like the linear force exerted by an ordinary spring. Indeed, this oscillatory motion is exactly like the motion of a mass attached to a spring.
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(C) 2005, Doug Davis; all rights reserved