This is not a HW/coursework problem. Just something I randomly thought about. 1. The problem statement, all variables and given/known data There is a horizontal spring with a mass at the end of it. The mass has an initial velocity V that compresses the spring. Find the equation of motion for this mass without using energy equations. 2. Relevant equations At any displacement X, force by spring is F = -kx Force on mass by spring = -m* (applied acceleration on mass by spring) = -ma Equation of motions: Vf^2 - Vi^2 = 2ax 3. The attempt at a solution As the displacement changes, then the force and hence acceleration provided by the spring against the mass is also changing. So acceleration against mass is function of distance. F = -kx = -ma a = kx/m Vf^2 - Vi^2 = 2ax <-- plug in a Vf^2 - Vi^2 = 2 (kx/m)x Vf^2 = 2 (kx/m)x + Vi^2 Did I do it right?