# Lengthening pendulum

## The Attempt at a Solution

Working with equation 18.1 i found that

However, this obviously is not the equation in 18.3.
http://file.scirp.org/pdf/JAMP_2014031310562629.pdf

I have no clue where to go with this problem. Where is the 2 d theata / dl term coming from?

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TSny
Homework Helper
Gold Member

## The Attempt at a Solution

Working with equation 18.1 i found that
Looks like you treated ##l## as a constant. But ##l## is a function of time.

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

But I am not familiar with how to treat L in this situation.

TSny
Homework Helper
Gold Member
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}##.

dykuma