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Condition of simple harmonic motion

  1. Jun 15, 2014 #1
    1. The problem statement, all variables and given/known data

    I was told that for an object to execute SHM, the x (distance displaced from the spring) cant be greater than e . Why is this so? i cant understand. can someone explain please?

    2. Relevant equations

    3. The attempt at a solution

    Attached Files:

  2. jcsd
  3. Jun 15, 2014 #2


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    First, you understand that 'e' here does not mean 2.7...., right? It's just the label being used for a variable.
    In the text you posted, it stands for the extension of the spring when the mass is hanging at equilibrium. When oscillating, the displacement x is relative to that equilibrium position, so the total extension of the spring is e+x.
    I do not see anywhere in the text that says x cannot exceed e, so I assume someone else said this. Suppose it does. In SHM, if the displacement is at times x then at other times it is -x. So if x can exceed e it will also happen that the total extension can go negative. Whether that's a problem depends on the type of spring.
    Many springs have an 'open' relaxed state. That is, they are capable of being compressed by some amount c before becoming closed up. For other springs, c = 0.
    SHM should occur provided x does not exceed e+c.
  4. Jun 16, 2014 #3
    well what happen if x exceed e ?
  5. Jun 16, 2014 #4


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    Haruspex explained that. The spring may stop working as a spring if |x| > |e|

    In your diagram..

    L0 = unstretched length of a tension spring.
    L0+e = the length with the mass at rest.
    x = displacement from L0+e

    If the vertical displacement x is greater than e the mass will rise to a position above L0 and the spring may stop working as a spring. Many tension springs don't work in compression.

    For example this type doesn't work in compression only tension..

    This type will handle compression but only up to a limit..

    Last edited by a moderator: Apr 28, 2017
  6. Jun 16, 2014 #5


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    Thanks for posting the two images. They explain it much better than I could in words.
    For the first image, it may even be true that it only works as a spring under sufficient tension. It may be effectively under tension before it is expanded at all.
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