Imagine a tunnel is cut completely through the earth that passes through its earth’s center. An object is dropped from rest at the surface of earth into this tunnel. Prove that the resulting motion is

Imagine a tunnel is cut completely through the earth that passes through its earth’s center. An object is dropped from rest at the surface of earth into this tunnel.

Prove that the resulting motion is periodic/the object undergoes simple harmonic motion.

What is the period for a 5 kg object?

Explain two changes you could make, with reference to your resultant algebraic

expression for period, that would shorten the period of the object.