Spring theory, when can this happen? If ever

flyingpig

1. The problem statement, all variables and given/known data

I have a spring on a horizontal flat frictionless surface. If I push it at its max at x = -x_max and releases it, will it stop at the equilbrium point and go back to x = -x_max or will it go beyond the x = 0 and go to x = x_max?

I know that if i have an object attched to the spring (but not becoming one with the spring) it will stop at x = 0 and releases it, but will it go back and forth between -x_max and x_max if there is no object?

lewando

Is your spring a real spring or an ideal (massless) spring?

flyingpig

hmmm let's go with the ideal massless spring

lewando

I imagine that if you compress/stretch an ideal massless spring and then release it, it would snap back to its neutral position instantaneously, with no oscillation. EDIT: oops, I meant to say it will oscillate from x_min to x_max at infinite frequency.

flyingpig

What if there is an object? Will it just stop at x = 0?

lewando

Yes. Recapping the scenario: an ideal massless spring on a frictionless horizontal surface is fixed at one side, equilibrium length is x. The spring is compressed to a length of x-x_max, and a mass is placed next to the compressed spring. At this point in time, the potential energy in the spring is given by:

PE_{-x_max} = (1/2)k(-x_max)²

As the mass-spring system is released the mass begins to accelerate towards the spring's equilibrium point, gaining kinetic energy. At the equilibrium point, there is no more PE in the spring. It has all been converted to the KE of the mass. The mass will continue moving, now at constant velocity. Since the spring is massless (no inertia) it will remain at the equilibrium point.