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Homework Help: Urgent: Simple gravity pendulum - don't understand it

  1. Dec 4, 2006 #1
    hi

    I know about harmonic oscilation, but I'm having trouble understanding how we derived formulas for gravity pendulum. Please read on.



    If a ball on a string ( string is attached to the ceiling ) is displaced from its equilibrium position by angle A1, then forces on this ball are force of string F[v] and F[g].

    F[v1] ... component of F[v] parallel to F[g] and of opposite direction to F[g]

    http://img473.imageshack.us/img473/1854/nihaloje2.th.png [Broken]

    BTW - if picture doesn't show up then please look at the attached jpg file





    1)

    a)
    Now why ( when angle A1 > 0 ) isn't the magnitude of F[v1] equal to F[g] --> F[v1] = -F[g]?


    b)
    I assume bigger the angle A, smaller is F[v1]. Why?
    I assume it's because F[v] is constant no matter what the angle A is, but why is that?





    2)
    According to my book angles A and A1 are the same:

    Code (Text):
    [B]F[net] = m * g * sin[A1]  =  m * g * sin[A][/B].
     
    I'd imagine angle A being the same as angle A1 only if F[g] = F[v1]. Then direction of F[net] would be horizontal. But since that is not the case thus the two angles shouldn't be the same.





    3)
    I will quote my book:




    a)
    I assume by that they mean to say that when arc L is twice as great, a isn't twice as great.
    But what has that got to do with harmonic osiclation? Is with harmonic oscillation a linear with L?
    Can you show me some proof of that?





    b)
    First of all, I'm not sure that sin[A1] and A1 are ever roughly the same size, since no matter how small A1 is, sin[A1] will always be 100 or more times smaller. Right?




    c)
    Second, even if sin[A1] and A1 have about the same value when A1 is small enough, what is the purpose of replacing sin[A1] with A1? Why do we want to do that?





    d)
    Also, why is acceleration vector a negative?
    I realise that when a has opposite direction to ball's velocity that it has to be negative. But sometimes ball's velocity and acceleration vectors have same direction and thus a should be positive?



    cheers
     

    Attached Files:

    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Dec 4, 2006 #2

    Hootenanny

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    Most of your questions can be answered by drawing a free body diagram. For question (a) consider what would happen if Fv1 = -Fg?
     
  4. Dec 4, 2006 #3
    Ball would start moving in a horizontal direction. I realise that and I know this is not the case, but why doesn't it happen?!
     
  5. Dec 4, 2006 #4
    Um if your angle keeps increasing it eventually reaches 90, so it keeps getting smaller and when it reaches 90 it goes to zero and tension is only determined in x direction since your tension component is basically Tension*cos(theta). I hope that answered the angle part of your problem
     
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