Calculating time period in vertical circular motion

[taninamdar]

1. 1. Homework Statement :
How to calculate minimum time period 't' required to complete a vertical circular motion by a cone filled with water, so that the water doesn't fall?2. Homework Equations :
v^2 = gR * [ 3 + 2 cos (theta) ] obtained by applying law of conservation of energy.

3. 3. The Attempt at a Solution :
I have found that v^2 = gR * (3 + 2 cos theta ). But the velocity varies with theta. So, how to calculate the time required to complete one revolution using variable velocity?

Thanks!

 

[taninamdar]

You can see the similar thread here, actually it has given more appropriate explanation than me, but still the thread is unsolved.
https://www.physicsforums.com/showthread.php?t=389744

 

[collinsmark]

Hello Taninamdar,

Welcome to Physics Forums!

You might want to research "Elliptic Integral of the First Kind," perhaps. Good luck!