If I remember right, if a hole were bored all the way through the center of the Earth and an object of sufficient tolerance to temperature, etc,were dropped in the hole, it would have a period of oscillation of 84 minutes. BTW that is also the period of a satellite at the surface of the (smooth) Earth. In addition, a pendulum of infinite length, with its mass swinging at the surface of the Earth, would have a period of 84 minutes. You're welcome...
Let's see.... I'll have to get out my infinite tape measure.
Are you talking about Schuler oscillation? Sounds familiar.