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Can somone explain this review solution (vibrations)?

  1. Apr 30, 2017 #1
    1. The problem statement, all variables and given/known data
    Capture.PNG

    2. Relevant equations
    The equations are all given

    3. The attempt at a solution
    This isn't really a hw question... it's solved, but i'm having a hard time following it. I don't understand where the first term:
    -a(kaθ)

    comes from. I can see it's the moment relation between the hinge and the spring but why is the a term squared?
     
  2. jcsd
  3. May 1, 2017 #2

    Nidum

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    Gold Member

    upload_2017-5-1_12-6-29.png


    Value 'a' is used to relate the force generated by the spring to the angle θ and as the lever arm length for the moment about the pivot generated by the spring force .
     
    Last edited: May 1, 2017
  4. May 1, 2017 #3
    Looking at it again. I'm sorry. I think my problem was just misreading the answer.
    Value a just the value used to reference the length? (6in)

    This would make:
    F spring = xk
    x = aθ

    Thus a(kaΘ) = M
    And it's negative because the fbd assumes the weight is tending CW while the weight and the spring force tend CCW?
     
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