A hole is drilled straight through the center of the planet Foosbane. The planet is remarkable in that its density is constant, independent of depth. Suppose a pebble is dropped into the hole. Neglecting rotational effects, show that the pebble undergoes simple harmonic motion, and determine the period.
If the radius of Foosbane is equal to the radius of the Earth, and the acceleration due to gravity at the surface is 5.4 m/s2, what is the period of oscillation of the pebble, in minutes?