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B Confusion About Oscillating Mass

  1. Jun 4, 2017 #1
    I'm sure there's an obvious answer to this, but this problem has been confusing me for some time.

    Imagine there were a massive object attached to the end of a crankshaft. A force is applied to accelerate the crankshaft, causing the mass to oscillate. Assuming there is no friction, what would happen to the system when the force is no longer applied? It shouldn't be possible for it to slow down if there's no energy loss, but wouldn't it require a force to continue to accelerate the mass back and forth?
     
    Last edited: Jun 4, 2017
  2. jcsd
  3. Jun 4, 2017 #2
    picture is needed
     
  4. Jun 4, 2017 #3
    I'm not exactly sure what you're looking for, but this is the basic idea.

    crankshaft.png
     
  5. Jun 4, 2017 #4
    the system will oscillate This is a Hamiltonian system with one degree of freedom
     
  6. Jun 4, 2017 #5
    And it will continue to oscillate at the same rate even when the torque is no longer applied?
     
  7. Jun 4, 2017 #6
    What does the "rate" mean? This will be nonlinear oscillation. Is gravity applied?
     
  8. Jun 4, 2017 #7
    I mean the frequency of the oscillation of the mass. I don't understand what you're asking.
     
  9. Jun 4, 2017 #8
    The motion of the system will be periodic
     
  10. Jun 4, 2017 #9

    Ibix

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    One thing to think about that may not have occurred to you - whatever your axle is attached to will also wobble so that the centre of mass does not move. This is analogous to the Earth-Moon system, which revolves around a point (the barycentre) slightly offset ftom the centre of the Earth.

    Does that help?
     
  11. Jun 4, 2017 #10
    I should have mentioned that. It would make sense not to include gravity just for the purpose of simplifying things, I suppose.
     
  12. Jun 4, 2017 #11
    that is wrong
    ok anyway the motion will be periodic
     
  13. Jun 4, 2017 #12

    Ibix

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    How is momentum conserved if the centre of mass moves?
     
  14. Jun 4, 2017 #13
    who does say that momentum conserved?
     
  15. Jun 4, 2017 #14
    How can momentum not be conserved? I assume that even if the mechanism were fixed on the earth, it would cause the earth to oscillate very slightly in response (as ibix described).
     
  16. Jun 4, 2017 #15
    Oh if you include the Earth in the system then I withdraw my objections :)
     
  17. Jun 4, 2017 #16
    I think that makes sense, but I still have one more question which relates to the initial purpose of this thread.
    I was trying to calculate the torque required to oscillate the mass at a constant frequency. So I found the velocity of the mass, and I then found the derivative, which gave me the acceleration. This allowed me to find the torque at the point in which the velocity of the mass was zero and the acceleration was at its maximum. (It gave me τ=Mω^2l^2, in which l is the length of the short rod). However, it doesn't seem to make sense to calculate this when there isn't any torque required to maintain that constant oscillation. I can't seem to reconcile this confusion with the explanation.
     
    Last edited: Jun 4, 2017
  18. Jun 4, 2017 #17

    A.T.

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    Are you assuming that all parts, except the block are masses? In that case the total energy is zero when the block is at rest, so the oscillation won't be maintained without an applied torque.
     
  19. Jun 4, 2017 #18
    Yes, I'm assuming all other parts are without mass. Isn't that contradictory to ibix's argument, or is this just a misunderstanding on my part?

    However, let's say the mass of the other parts were just extremely small. Would the frequency of oscillation decrease or remain constant over time?

    Also, how can there be no energy in the system if it was initially in motion and no energy was lost?
     
  20. Jun 4, 2017 #19

    A.T.

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    Your assumptions are obviously contradictory then.

    Without energy dissipation, constant.
     
  21. Jun 4, 2017 #20
    But can't you approximate what would occur in the system by considering the other parts without mass if the mass of those parts are in reality very small?
     
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