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Oscillation of a stick

  1. Sep 17, 2016 #1
    1. The problem statement, all variables and given/known data
    A meter stick is free to pivot around a position located a distance x below its top end, where 0 < x < 0.50 m(Figure 1) .

    2. Relevant equations


    3. The attempt at a solution
    I attached my note.
     

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  2. jcsd
  3. Sep 17, 2016 #2

    TSny

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    Your expression for ##I## about the axis of rotation looks correct to me. Although I think I would have just used ##I = I_{cm} + Md^2## with ##I_{cm} = \frac{1}{12} M L^2##.

    It appears to me that you have a mistake in the numerator of your expression inside the square root for ##\omega##. Review the general formula for ##\omega## and make sure you are interpreting the symbols correctly.
     
  4. Sep 17, 2016 #3
    I tried that approach but I failed. Am I annoying?
     

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  5. Sep 17, 2016 #4

    TSny

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    It should give the correct answer. If you show your work, we can identify any mistakes. Make sure you are interpreting ##d## correctly. ##d## also occurs in the numerator of ##\omega##.
    Not at all.
     
  6. Sep 17, 2016 #5
    I think d is the distance from the center to the pivot point which is (1/2 - x)
     
  7. Sep 17, 2016 #6

    TSny

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    Yes.
     
  8. Sep 17, 2016 #7
    Can you help me check out my steps please?
     

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  9. Sep 17, 2016 #8

    TSny

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    You are setting it up correctly, but you need to be more careful with simplifying the expressions. Try it again and take your time.

    Also, note that ##\frac {d^2\theta}{dt^2}## is not the correct notation for ##\omega ^2##.
    ##\frac {d^2\theta}{dt^2}## is the angular acceleration of the rotational motion.
    But ##\omega## is the angular frequency of the simple harmonic motion; i.e., ##\omega = \frac{2 \pi}{T}##, where ##T## is the period of the simple harmonic motion.
     
  10. Sep 17, 2016 #9
    Yes I know that. I will take a look tomorrow again for my expression. Thanks a lot. I appreciate it. Have a good night!
     
  11. Sep 17, 2016 #10

    TSny

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    OK. Good luck with it.
     
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