A particle P of mass m can slide along a smooth rigid straight wire. The wire has one of its points fixed at the origin O, and is made to rotate in the (x, y)-plane with angular speed Ω. Take r, the distance of P from O, as generalised coordinate and obtain Lagrange's equation. Initially the particle is a distance a from O and is at rest relative to the wire.
Find its position at time t. Find also the energy function h and show that it is conserved even though there is a time dependent constraint.