Cavern

Score: 3 Points

Suppose, in your nightmare, you have been thrown to a cylinder-shaped hole which is as long as the diameter of the earth and goes through the center of the Earth. If this nightmare occurs, in reality, you will oscillate at a certain frequency about the center of the Earth.



What is the period of this oscillation?
Your answer should be in second. Don't insert the unit.
Assume that,
$R_E=10^5m$
$g=10\frac{m}{s^2}$
$\pi=3.14$


Image source: Fall through the earth