[QUE/CM-02033]

A bead of mass \(m\) slides on a frictionless wire under the influence of gravity and the shape of wire is parabolic with axis begin along the vertical upwards. The wire rotates about the its axis, (\(z\)- axis), with constant angular velocity \(\omega\). Take \(z^2= a\rho\) as equation of the parabola.

1. Set up Lagrangian and obtain equations of motion.
2. Obtain the Hamiltonian. Is the Hamiltonian equal to energy? Is Hamiltonian or energy or both are constants of motion?