The gravitational force on a particle of mass m inside the earth at a distance r from the center (r < the radius of the earth R) is F = −mgr/R (Chapter 6, Section 8, Problem 21). Show that a particle placed in an evacuated tube through the center of the earth would execute simple harmonic motion. Find the period of this motion.

The gravitational force on a particle of mass m inside the earth at a distance r from the center (r < the radius of the earth R) is F = −mgr/R (Chapter 6, Section 8, Problem 21). Show that a particle placed in an evacuated tube through the center of the earth would execute simple harmonic motion. Find the period of this motion.