1. The problem statement, all variables and given/known data At which point does the mass on a vibrating spring have its largest velocity? Smallest velocity? 2. Relevant equations Hooke's Law? See below. 3. The attempt at a solution I know the mass on a vibrating spring has the greatest acceleration when the greatest amount of force is acting on the mass. So at the two endpoints of the motion, where the spring is either stretched or compressed the most. We know this because of Hooke’s Law. Hooke’s Law= the further the spring is displaced from its equilibrium position (x) the greater the force the spring will exert in the direction of its equilibrium position (F - restoring force). And the acceleration is smallest at the midpoint of its motion, so equilibrium. But what about velocity? Smallest velocity would be at the endpoints of motion too, because for that one instant it's not moving? Edit: Afterthought- would it possibly have something to do with potential or kinetic energy at a certain point in its motion?