Sir if the pendulum is given an angular velocity about the -he z axis then whether eq 1 is right for balancing force and I have a contradict regarding eq 2 and eq 3[/B]
I think you are marking too many forces on your diagram.
When you resolve a force into components, you are saying those components are equivalent to that original force. They don't add to it.
You can replace a force by two orthogonal components, but you can't keep taking more bits in other directions.
Identify clearly the actual forces, then in your calculations, use their components to produce balanced equations.
It might even help to say for each equation, what direction you are looking at.
