What If You Dug a Tunnel Through the Earth?

What would happen if Elon Musk (that guy is cool) dug a tunnel through the center of the Earth? We'll assume the materials can withstand the absurd temperatures at the Earth's core and that we can pump the air out of the tunnel. If you pumped the air out, you'd get to the other side in 42 min. With air (not treated in the video) it would take well over a day and a half if your terminal velocity was 200 mph. This video shows how the form of Newton's Law of Gravitation leads to simple harmonic motion - just like that of a mass on a spring. The key here is that the relevant mass for attracting the falling object is the mass of the Earth that is between the Earth's center and the current location of the falling object.