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Vibration Massless spring static equilibrium

  1. Oct 14, 2014 #1
    Let us imagine that there is a Massless spring with fixed at one end.

    Unloaded length = L

    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 ?

    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.
  2. jcsd
  3. Oct 15, 2014 #2


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    Gold Member

    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!
  4. Oct 15, 2014 #3
    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.
  5. Oct 15, 2014 #4


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    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.
  6. Oct 15, 2014 #5
    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..
  7. Oct 15, 2014 #6
    I was thinking about another possibility, but as we are in classical physics you are right.
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