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I Does a perfect spring oscillate forever in gravity?

  1. Dec 5, 2016 #1
    Suppose you have a perfect spring. By that I mean a spring that experiences no friction whatsoever, even internal, and that there is no elastic limit. Thus it obeys Hooke's law perfectly. Its own weight is negligible, and there is a point mass attached to the end of the spring.
    Now, the spring is held horizontally at first in Earth's gravitational field and is turned vertically suddenly. Gravity will exert a force on the spring, and the spring will extend, till the point where its own force balances that of gravity, shifting the equilibrium point of the spring.
    However, in reaching its new equilibrium point, the spring must have picked up velocity from gravity. While the force at equilibrium is zero, the velocity is not, and the spring should continue oscillating as if it were disturbed from equilibrium.
    My question is if this oscillation is constant. Will the spring continue oscillating forever with the same amplitude?
    Also, if this is the case, is friction in the spring and the surroundings the reasons why this is not observed? Or is it just one source of friction?
    Thanks for any answers
     
  2. jcsd
  3. Dec 6, 2016 #2

    Nugatory

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    Yes. You can get this result from conservation of energy.
    Well, "the surroundings" means "outside the spring", and between that and inside the spring, there's nowhere else to look for other sources of friction.
     
  4. Dec 6, 2016 #3
    Alright thanks for the answer
     
  5. Dec 6, 2016 #4

    Nidum

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    @albertrichardf

    If you observed the motion of an imperfect suspension spring and mass system in a real world environment and over a long period what might you expect to see ?
     
    Last edited: Dec 6, 2016
  6. Dec 6, 2016 #5
    I would expect an initial oscillation, that would eventually decay.
     
  7. Dec 6, 2016 #6

    Nidum

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    The motion never actually comes to a complete stop - why do you think that is ?
     
  8. Dec 6, 2016 #7
    You mean the spring continues oscillating forever? Is that actually the case? Because I would have though that the friction would dissipate energy from the spring, hence reducing the amplitude till the amplitude becomes zero. I actually don't see how the spring could be in motion.
     
  9. Dec 7, 2016 #8

    Nugatory

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    When we model the spring as an ideal spring that loses a fraction of its energy on each oscillation, you're right - we get a differential equation that says that the motion never stops completely. However, that model breaks down as the energy of each oscillation becomes smaller and approaches the random thermal energy of the atoms making up the spring. Real non-ideal springs do stop oscillating eventually.
     
  10. Dec 7, 2016 #9

    Nidum

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    @Nugatory

    What I was encouraging @albertrichardf to think about was what happens to the motion of a real spring mass system in a real environment .

    Perturbations from the environment are usually sufficient to sustain small amplitude motion of any mechanical system which is capable of oscillation and which is not heavily damped or actively controlled in some way .

    Usually the perturbations come from sources like air currents , ground movements , thermal expansion or stray magnetic fields .

    With a real spring mass system the large scale oscillation will usually die away quite quickly but there is always going to be some residual component of oscillation maintained by these perturbations . At this small scale of movement the actual motion is often complex and continually mutating from one mode to another .

    Study of this problem has application in the design of sensitive and/or precision equipment .
     
  11. Dec 7, 2016 #10
    All right. Thanks for the answers. I was talking about large-scale oscillations though, those that are readily visible to the naked eye. It is interesting though to find out about smaller-scale perturbations from the environment.
     
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