Vibration Massless spring static equilibrium

[Gunmo]

Let us imagine that there is a Massless spring with fixed at one end.

Unloaded length = L

Spring constant: = k

Mass = 0The spring is at static Equilibrium

Force: F

Displacement: d

F = k d,
elongated length: L+d


If I remove F, what will happen ?

1. Spring return to the original length: L and Stop moving

2. Spring length vibrate between "L - d" and "L+d"

Note: there is no mass, damping, friction.

 

[ShayanJ]

Its possible to think and give some answers but it seems to me that they will be non-sense. And because this question is actually useless and non-physical (there is no massless spring!), I think its better that you don't ask this question and don't face such non-sense answers because of nothing!

 

[PaulDirac]

When you remove the force F it gets vibrating around the equilibrium point L and keeps so provided there is no dissipating forces like the air resistance to deplete the vibrational energy of the spring.

 

[Nugatory]

When you remove the force F it gets vibrating around the equilibrium point L and keeps so provided there is no dissipating forces like the air resistance to deplete the vibrational energy of the spring.

That's what any real spring would do, but OP has carefully specified a massless spring. As Shyan says, there is no solution in that case - we're applying a non-zero force to a zero mass and that situation is unphysical.

 

[PaulDirac]

I understand. I was assuming that there is still a little mass in order to involve it in the vibration. Otherwise, it is nonsense to think of vibrating a massless spring. But I don't think that is what he means, i.e. we don't have any physical spring to be totally massless. By M = 0 I think he means an infinitesimal mass, say of order epsilon, though. He should specify..

 

[DrStupid]

we're applying a non-zero force to a zero mass and that situation is unphysical

I was thinking about another possibility, but as we are in classical physics you are right.