Finding the differential equation for a oscillating system

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The discussion revolves around deriving the differential equation for an oscillating system, with specific focus on the forces involved. Participants express confusion over the presence of a constant mg term instead of the expected mgsinθ, which typically simplifies to mgθ under small angle approximations. There is a repeated concern about the lack of distance variables in the moment expressions, leading to uncertainty in the calculations. The need for clearer working steps is emphasized for those seeking further assistance. Overall, the thread highlights common pitfalls in applying small angle approximations and the importance of including all relevant variables in the equations.
JustinLiang
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Homework Statement


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The Attempt at a Solution


I don't think this is the correct answer because for some reason I have a constant mg term. Usually I get mgsinθ and from small angle approximations it becomes mgθ, but this time I am getting mgcosθ and from small angle approximations it becomes mg.

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What am I doing wrong? Or is this correct?
 
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I don't see the distances in your expressions for the moments.
 
haruspex said:
I don't see the distances in your expressions for the moments.

I just tried this question and did it with the distances, but I also don't understand why there is a constant term. That term is throwing me off.
 
theBEAST said:
I just tried this question and did it with the distances, but I also don't understand why there is a constant term. That term is throwing me off.
Please post your working if you'd like further assistance.
 

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