The solution to this problem was not so hard .The required knowledge can be found on the Internet but In this case I myself solved.

You could say that your equation with a good approximation is correct . Details in the file. And then there's one thing I'm not an expert . Only an engineer.

Attachments:

Thank you, Mariusz, keep the good posts coming!

Hello,

I am new to Mathematica and was going through a few simulations and animations, and trying a few things like Rotations and Transformations.

I had one doubt, is there any way to rotate the bowl along a certain axis while the marble is moving inside it at the same time?

Will a Rotate function like below used inside Initialization work?

Rot[\[Alpha]_] := {{Cos[\[Alpha]], -Sin[\[Alpha]]}, {Sin[\[Alpha]], 
     Cos[\[Alpha]]}}
   Rot1 = bowl
   Animate[
    Graphics[GeometricTransformation[Rot1, Rot[\[Alpha]]], 
     Axes -> True], {\[Alpha], 0, 2 \[Pi]}]

Thanks