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Calculating error in pendulum motion

  1. Feb 5, 2017 #1
    1. The problem statement, all variables and given/known data
    I have to calculate the propagated error on g of pendulum. I pretty much measured the T of pendulum and now calculating g while increasing the number of cycles.

    2. Relevant equations
    I used the equation of propagated error and i included picture of it and my calculations.

    3. The attempt at a solution
    I plugged all the values into the equation but what bothers me is the size of the error. For 20 cycles I get g=9.776, but my error is 0.02. This seems like a huge error, and would mean that my g would equal to 9.78. Anyone sees any mistake?
     

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  2. jcsd
  3. Feb 5, 2017 #2

    TSny

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    To avoid a crick in the neck
     

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  4. Feb 5, 2017 #3
    Thanks! Makes it more convenient.
     
  5. Feb 5, 2017 #4
    Here is picture of the equation and detail calculations.
    * I don't know how to rotate the picture, sorry.

    Edit: Image rotated by moderator:

    Pend Calc.JPG
     

    Attached Files:

  6. Feb 5, 2017 #5

    gneill

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    Staff: Mentor

    Most platforms have ways to rotate an image. What type of computer are you working from?
     
  7. Feb 5, 2017 #6

    TSny

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    I don't see any mistakes (but I didn't check all your calculations). Why do you think your error is "huge"?
     
  8. Feb 5, 2017 #7
    Here, I figured it out.
     

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  9. Feb 5, 2017 #8
    Well I think it's huge because it would mean that I can trust my g only to 3 sig figs. So I pretty much throw away one sig fig.
     
  10. Feb 5, 2017 #9

    TSny

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    3 sig figs seems OK to me. For 20 cycles you have a fractional error in T of about .001/1.44 ≅ .0007. But note that T is squared in the formula for g. So, the contribution of the error in T to the relative error in g should be roughly 2(.0007) ≅ .001. The contribution of the error in L to the relative error in g is roughly .0006/.51 ≅ .001. So, I don't think it's surprising that when you use your more accurate formula to determine the error in g, you find that you are only getting 3 sig. figs. for g.
     
  11. Feb 5, 2017 #10

    TSny

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    upload_2017-2-5_14-17-45.png
    You made an error in grinding the numbers here.
     
  12. Feb 5, 2017 #11
    Wow. Thanks a a lot. Now it makes way more sense for that cycle.
     
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