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Which of the following is not essential for SHM

  1. Jun 26, 2011 #1
    Which of the following is not essential for SHM?
    a) restoring force
    b) gravity
    c) elasticity
    d) inertia
     
  2. jcsd
  3. Jun 26, 2011 #2

    Doc Al

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    What do you think and why?
     
  4. Jun 26, 2011 #3
    I think its gravity
    Simple harmonic motion requires a restoring force, as that brings the objects back to the equilibrium position. It requires inertia, as that keeps the object moving through equilibrium, resulting in harmonic motion. It requires elasticity, as that is the source of the restoring force, it's the 'k' value, as it were. Elasticity results in the spring constant. Gravity, however, is not necessary. While it may be necessary for pendulum harmonic motion, as it results in the restoring force there, simple harmonic motion can be just a ball on a spring resting on a horizontal frictionless table. Pull the ball, it will have simple harmonic motion until the end of time, with no gravity acting on it.
     
  5. Jun 26, 2011 #4

    Doc Al

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    Good answer! :approve:

    Edit: Oops! See gneill's correction.
     
    Last edited: Jun 26, 2011
  6. Jun 26, 2011 #5

    gneill

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    Where's the elasticity in a pendulum?:devil:
     
  7. Jun 26, 2011 #6

    phinds

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    That's beside the point. The question was which of these can you omit and still HAVE SHM, not "are there any of these that would break SLM in SOME cases".
     
  8. Jun 26, 2011 #7

    gneill

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    The question is, "which is not essential for SHM". Do pendulums exhibit SHM? Is there elasticity in the pendulum system? If your answers are "yes" and "no" respectively, then elasticity is not essential for SHM.
     
  9. Jun 26, 2011 #8

    Doc Al

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    Good point, gneill. (You devil, you! :wink:)
     
  10. Jun 26, 2011 #9
    its a stupid A level question, thats why theres no completely correct answer. I would say the correct pick would be inertia
     
  11. Jun 26, 2011 #10
    So its elasticity for a simple pendulum and gravity for a horizontal spring system. :approve:
     
  12. Jun 26, 2011 #11

    Doc Al

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    Evaluate each choice by asking: Is it possible to have SHM without this?
     
  13. Jun 26, 2011 #12

    ehild

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    Pendulum motion is not really shm, but there are cases for shm where elasticity is not essential.

    ehild
     
  14. Jun 26, 2011 #13

    I like Serena

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    Hmm, I thought the motion of a pendulum is not SHM.
    It is only SHM by approximation. :)

    However, motion by elasticity does show SHM.

    Edit: I think answer (c) should be: elasticity-like force, since that is required and not contained in the other answers.
     
  15. Jun 26, 2011 #14
    :O
    you sure u didnt just have a really bad day or one of ur friends died or something?
     
  16. Jun 26, 2011 #15
    sure if u have a really stiff spring it will also not undergo SHM no matter how hard u press
     
  17. Jun 26, 2011 #16

    gneill

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    For small angular displacements the motion of a pendulum approximates very closely to SHM, and it is often taken as such in introductory level courses. I judged that this would be the case given the apparent level of this question and the forum it's posted in... I am, of course, always open to corrections :smile:
     
  18. Jun 26, 2011 #17
    The fact that it is Simple only means it is valid to some approximation. The fact that it is harmonic motion applies to pendulums, springs, car breaks, anything of the kind. but not all of them are simple. pendulums motions are SHM, as discovered first by galile.
    inertia is not required for SHM because light is the most important case of SHM and it has no inertia. otherwise gravity, elasticity or restoring forces are all encountered in SHM systems as essentials parts contributing to the motion being harmonic.
     
  19. Jun 26, 2011 #18

    I like Serena

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    Yeah, so the answer should be "inertia-like behavior", which is required and not contained in the other answers.
    But then, it's only an A level question.

    And no, as you can find in for instance the http://en.wikipedia.org/wiki/Simple_harmonic_motion" [Broken], simple harmonic motion does not mean it is simple by approximation.
     
    Last edited by a moderator: May 5, 2017
  20. Jun 26, 2011 #19
    in deriving the equation of motion for simple harmonic oscillators, one takes the assumption that F=-kx
    where k is the constant of proportionality that connects the motion of the particle to the rigidity of the oscillator. this assumption, that the rigidity of the oscillator is constant is the reason why you call it a simple system, because you are ignoring the second and higher order terms in rigidity. otherwise the word simple will take no meaning whatsoever
    as you can see here
    http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/Oscillations2.htm
    or else in any textbook, you can see that in general F does not equal a constant but also depend on dx/dt. which is why the word simple implies an approximation to a system where there is no damping, or second order torque terms as well as higher order rigidity terms.
     
    Last edited: Jun 26, 2011
  21. Jun 26, 2011 #20

    ehild

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    ??????????? :frown:

    Consider the case of a floating box in water when it is pushed a bit downward from its equilibrium position and released.

    Consider the case of a body falling in a tunnel drilled across the Earth through its centre. (well, not quite practical example)

    These are mechanical examples for shm without elasticity.

    ehild
     
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