Tunnel

Using equivalent Gauss Law for gravitation,
Let the distance of the ball from the centre of the earth be x Let the mass density of the earth be uniform
Then ∫EdS = 4∩Gm_in
As E is symmetrical,
E*4∩x² = 4∩G*ρ*4/3 ∩x³
=> E = 4∩Gρx/3 = a
So as a = -kx (using vectorial relation)
so the motion is SHM with amplitude equal to the radius of the earth

almost an universally known thing :
shm.....with time period of 84.6 minutes !