1. The problem statement, all variables and given/known data 2. Relevant equations http://en.wikipedia.org/wiki/Simple_harmonic_motion 3. The attempt at a solution So I labeled the image at the points of interest where I would need to calculate certain values. for part a) so from A --> B All I'm trying to figure out here is how fast the object is going before collision, using conservation of energy I am able to the final velocity of the object by finding the change in potential energy. B -- > C Since it is a perfectly inelastic collision, I would know that momentum is conserved which will lead me to find the final velocity the combined object is going after collision, with that using momentum conservation laws, mVo = (m + 4m)Vf C -- > D again, conservation of energy is applied but this time with potential spring energy, which I have set up as, KEinitial = PEspringF Since I have found the velocity, all I am solving for is X which would equal to the amplitude(A) that the spring undergoes. Once I have found that, I know that the general term for position as a function of time in a harmonic system is x(t) = Acosθ part b) I need a clue on this one, Am I to just compare the initial potential energy of mass m to the potential spring energy?