1. The problem statement, all variables and given/known data This was a test question I had today but basically, initially the mass is at rest as the buoyant force opposes the force of gravity. Then we push it down X meters and let it go. This can be described by SHM. We are also given the density of water, a cross sectional area of the mass, and the actual mass, M. 2. Relevant equations A=area (not amplitude) X_0= equilibrium position X_new= furthest value it can be bobbed up or down Archimede's Principle 3. The attempt at a solution Net force=mg-A*(X_0+X_new)*rho_w*g note that this is zero at the equilibrium point where X_new equals 0. ma=mg-A*(X_0+X_new)*rho_w*g a=g-(A*(X_0+X_new)*rho_w*g)/m The general form of a SHM equation is x(t)=Acos(ωt) which can be solve to x''(t)=-ω^2Acos(ωt) I assumed ωt to be 0 so as we are using the amplitude. We know the amplitude to be X_0+X_new however I chose X_0 to be zero for simplicity (I know this isn't correct as the volume would be zero but this was just the position). Thus, the amplitude is now X_new. I then set the acceleration equal to x''(t) to solve for ω: g-(A*X_new*rho_w*g)/m=-ω^2X_new ω=sqrt(-g/X_new+(A*rho_w*g)/m) If anyone can confirm this, that'd be awesome!