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Simple harmonicmotion

what is the relation between the energy &time period of a pendulam while not considering the small angle approximation,the given potential v(x)=Asinx
 

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this is a pretty straightforward question. u just hav to turn more mathematical cranks. u will find this worked out probably in Kleppner or in Purcell.
U get some sort of elliptic functions ( most probably)
 
16
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sorry i mentoined the book wrong it should be Berkeley mechanics( Kittel) not purcell/ it was a slip of mind and i apologise
 

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