What happens when you throw a ball thrown through a hole dug through the center of Earth?

At first when you the ball falls through and passes the center and proceeds further away from the center to the other side due to the momentum. Then the ball falls back to the center and with that momentum it again passes back through the center of Earth and back to the side. This repeats and this kind of motion is known as SHM.

Simple harmonic motion is typified by the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's Law. The motion is sinusoidal in time and demonstrates a single resonant frequency.