Simple pendulum - displacement increase

AI Thread Summary
The discussion centers on calculating the time taken for a simple pendulum's angular displacement to increase by a factor of 10, with the proposed solution being approximately (l/g)^(1/2)ln20. Participants are exploring the use of the general solution x=½Ae^(pt)+½Be^(-pt) from Kibble's chapter 2, but there is uncertainty about how this relates to the desired outcome. There is a request for guidance on both the mathematical approach and how to format equations for clarity in posts. The conversation emphasizes the need for clear communication and effective problem-solving strategies in physics discussions. Overall, the thread seeks to clarify the relationship between the equations of motion and the specific time calculation for the pendulum.
ward.o.j
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<Moderator's note: Moved from a technical forum and therefore no template.>

A simple pendulum of length l (supported by a light, rigid rod) is released from rest at a small angle to the upward vertical.

Show that the time taken for the angular displacement to increase by a factor of 10 is approximately (l/g)1/2ln20.

This is from chapter 2 of Kibble. There's a section which suggests writing x=½Aept+½Be-pt as one version of the general solution to the equations of motion which seems promising, but I can't see how this leads to the value in the question, or if I'm just barking up the wrong tree.

Any advice on how to proceed would be much appreciated.

P.S. If anyone would like to shed some light for me on how to post equations so that they are more readable than the one's I've posted, I'd be grateful for that as well.
 
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Please show us a little bit more than just an equation which might help. What equations have you tried so far, i.e. which was the tree you were barking at?

For on how to write formulas, you might want to read our introduction:
https://www.physicsforums.com/help/latexhelp/
 
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