# Vibration Massless spring static equilibrium

1. Oct 14, 2014

### Gunmo

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

Spring constant: = k

Mass = 0

The spring is at static Equilibrium

Force: F

Displacement: d

F = k d,
elongated length: L+d

If I remove F, what will happen ?

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

Note: there is no mass, damping, friction.

2. Oct 15, 2014

### 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!

3. Oct 15, 2014

### 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.

4. Oct 15, 2014

### Staff: Mentor

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.

5. Oct 15, 2014

### 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..

6. Oct 15, 2014

### DrStupid

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