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From: Narasimham on 16 Feb 2010 06:12
continued..

(* You are attempting to use advanced CAS Mathematica perhaps
without adequate prior paper and pencil work.

Letting {x,y}=R {Cos[th],Sin[th]} ; dt =ds /Sqrt[2 g y] ; dt/dth= -
Sqrt[R/2g]/Sqrt[Sin[th]] ;

the time integrates to Sqrt[2R/g]*EllipticF[th/2,2] in terms of
Elliptic Integral ;

A particle takes ~ 2.6 seconds from top to bottom in a circle of
diameter 9.8 meters

*)

t= Integrate[-1/Sqrt[Sin[th]],th]

2 EllipticF[1/2 (Pi/2-th),2]

Plot[% ,{th,0,Pi}]

HTH

Narasimham

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