1. The problem statement, all variables and given/known data Two masses m1 and m2 are connected to a spring of elastic constant k and are free to move without friction along a linear rail. Find the frequency of oscillatory motion of this system. 2. Relevant equations m1a1 = -m2a2 3. The attempt at a solution There is equal and opposite force, so momentum is conserved. The force on each mass is proportional to k. I choose a coordinate system to aid in formulating the following differential equations: m1x1''=-k(l0 - x2 + x1) m2x2''= k(l0 - x2 + x1) where x1,2 indicates the respective masses position and l0 is the spring equilibrium length. Is this a correct approach so far? If so, I have never solved differential equations of this type. How would one find x1, x2? Perhaps I am going about this wrong all together.