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Simple pendulum (SHM) problem

  1. Jun 30, 2012 #1
    1. The problem statement, all variables and given/known data
    attachment.php?attachmentid=48776&stc=1&d=1341063270.gif
    Consider, as shown in the picture, a penulum of mass m=0.52g, hanging on an ideal rope of length l=0.31m. A force is exerted to this pendulum as shown in the picture.
    The horizontal component of the force is:
    [tex] \displaystyle {{F}_{x}}={{F}_{0}}\cos \left( \omega t \right)[/tex]
    [tex] \displaystyle {{F}_{0}}=2.3N[/tex]

    Calculate the angular frequency that will make the system oscilate with the maximum amplitud. Consider small oscilations around the equilibrium position.

    2. Relevant equations



    3. The attempt at a solution

    I did nothing beucase I don't know how to deal with that variable force. BUT, what I did was to use the angular frequency of a simple pendulim which is
    [tex] \displaystyle \sqrt{\frac{g}{L}}[/tex]
    And I just replaced the values and I got the correct answer! 5.6rad/s.
    But my question is: why did I get the correct result if there's a force there?

    Thanks!
     

    Attached Files:

  2. jcsd
  3. Jul 1, 2012 #2
    Hi Hernaner28! :smile:

    Your method works because the frequency you used is the natural frequency of the system. And any body vibrates with a greater amplitude when externally forced to vibrate with its natural frequency(Resonance)
     
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