1. The problem statement, all variables and given/known data A particle of mass m is dropped into a hole drilled straight through the center of the Earth. neglecting rotational effects and friction, show that the particle’s motion is a simple harmonic if it is assumed that the Earth has a uniform mass density. Obtain an expression for the period of oscillation. 2. Relevant equations The answer is that K = (4/3)Gmπρ and so T = sqrt(3π/Gρ), right? K = force constant G = gravitational constant ρ = density of earth m = mass of object dropped T = period 3. The attempt at a solution I want to know why the constant K is not actually GmM/r3 and the force is not GmMx/r3 where x is the displacement of the object from equilibrium at any point within the earth (I defined equilibrium to be at the center of earth). I think my issue is not understanding what it means to solve a problem using uniform density. I thought that uniform density meant that the mass per unit volume was the same everywhere in the earth, so the constant M is okay to leave in the equation since it's density is not changing. I want to understand this because there is a problem in my homework set which asks to find the electrostatic potential energy of a sphere of uniform density with charge Q and radius R. My mind tells me this is simply Q2/4πεR... but that can't be correct because it's too easy and that is the same as a point charge. What am I not getting?