A tunnel through the Earth. If you’re ever on a Sunday walk and you stumble upon a hole in the ground that turns out to be a tunnel to the other side of the Earth, it would be a jolly good time to drop an object in the hole….as long as its not a cherished possession/living being. If air resistance isn’t much of a factor, you’ll find that the object will return to you…eventually. An object in a “center of Earth tunnel” is a harmonic oscillator and will move in a similar fashion to a mass attached to a spring.
In this case, the “spring constant” is: k=mg/R(Earth) where m is the mass of the object you dropped, g is the acceleration due to gravity at the Earth’s surface (g=9.80 m/s^2 ), and R(Earth) is the radius of the Earth (radius of earth=6,378,100 meters).
So let’s say you “accidentally” dropped your textbook in this tunnel. How long would it take for it to make its way back to you?
