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Lengthening pendulum

  1. Oct 31, 2016 #1
    1. The problem statement, all variables and given/known data
    upload_2016-10-31_21-12-40.png
    2. Relevant equations
    upload_2016-10-31_21-13-2.png
    3. The attempt at a solution
    Working with equation 18.1 i found that
    upload_2016-10-31_21-18-20.png
    However, this obviously is not the equation in 18.3.
    I found a source talking about this problem, and they get a similar equation
    http://file.scirp.org/pdf/JAMP_2014031310562629.pdf
    upload_2016-10-31_21-20-56.png
    I have no clue where to go with this problem. Where is the 2 d theata / dl term coming from?
     
  2. jcsd
  3. Oct 31, 2016 #2

    TSny

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    Looks like you treated ##l## as a constant. But ##l## is a function of time.
     
  4. Oct 31, 2016 #3
    Hmm. I was assuming that it was a constant before I made the substitution, I see the flaw in my logic there. So then I need to leave it in this form upload_2016-10-31_21-46-26.png
    But I am not familiar with how to treat L in this situation.
     
  5. Oct 31, 2016 #4

    TSny

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    In the expression ##\frac{d}{dt} \left(l^2 \cdot \frac{d\theta}{dt} \right)## it might help to replace the time derivatives with derivatives with respect to ##l## using your relation ##\frac{d}{dt} = v \frac{d}{dl}##.
     
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