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Scaling factor of a simple pendulum between length and time period.

  1. Jan 3, 2013 #1
    1. The problem statement, all variables and given/known data

    The time period of a simple pendulum is doubled when the length of the pendulum is increased by 3.0m. What is the original length of the pendulum?

    2. Relevant equations

    T= 2∏√(l/g)
    also l is original length and l+3 is the new length

    3. The attempt at a solution

    So
    2T=2(2∏√(l/g)
    2T=2∏√(4l/g)
    The new length is 4 times the original length and it also has to be the original length plus 3m.
    ∴ 4l=l+3
    so l=1m

    I am happy with the mathematical steps, and it gives me the correct answer.
    It is the reason why I can do this I could do with some guidance on.
    Is it because when I double T the only thing that could change is the length?
    Therefore I can put the multiplying factor of 2 inside the sqrt as 4×l.
     
  2. jcsd
  3. Jan 3, 2013 #2

    tiny-tim

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    hi mrcotton! :wink:
    yes, that's exactly right …

    T = 2π√(l/g) means that T is proportional to √l, so twice T means 4 times l (if everything else is the same) :smile:

    (and your proof is completely correct)
     
  4. Jan 3, 2013 #3

    rude man

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    What you did is fine. But you were lucky to have been able to sneak the "2" inside the square root sign so easily to make 4.

    I would have said

    T = 2π√(l/g)
    2T = 2π√[(l+3)/g]
    so 2 = √[(l+3)/l]
    & solve for l.
     
  5. Jan 3, 2013 #4

    tiny-tim

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    isn't that the same?
     
  6. Jan 3, 2013 #5
    Thanks ever so much for the help with getting my old grey matter working.
    So in general I can solve it like this.
    Q85_zps9e5c662b.jpg
    Did the sqrt of 4 only work for those values.
    I tried doing the calculation both ways for a pendulum thats time period has tripled when the original length is extended by 6m and got the same results.
     
  7. Jan 3, 2013 #6

    rude man

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    Yeah, maybe I was a bit severe here ... did you try for new l = 1.73l? This is a very trivial point, should probably not even have raised it.
     
  8. Jan 3, 2013 #7
    Hi Rude man, please I like the trivial points. Its the pedantic points in physics that make it interesting to me. Each physics question seems to open up more questions.
     
  9. Jan 3, 2013 #8

    rude man

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    OK I got plenty of those ... :smile:
     
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