I found something kinda cool
What happens when you cut a hole through the entire earth and drop something in that hole? You should get a harmonic oscillator right? I first tried to solve this for when the hole goes through the center of the earth, and the differential equation that models this is easy to find: force of gravity is proportional to the inverse square of the distance between object and the center of the earth so y''+1/y^2=0 when you set all constants equal to 1. Couldn't find an analytic solution so i used a computer and it turned into a vertical line when it hit y=0. This makes sense because the force at that point becomes infinite.
So i made a little modification to the problem to make it better solvable (numerically)

part 1, there is more to this