Lengthening pendulum

  • Thread starter dykuma
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  • #1
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Homework Statement


upload_2016-10-31_21-12-40.png

Homework Equations


upload_2016-10-31_21-13-2.png

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?
 

Answers and Replies

  • #2
TSny
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The Attempt at a Solution


Working with equation 18.1 i found that
upload_2016-10-31_21-36-53.png
Looks like you treated ##l## as a constant. But ##l## is a function of time.
 
  • #3
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Looks like you treated ##l## as a constant. But ##l## is a function of time.
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.
 
  • #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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