A bead slides along a smooth wire bent in the shape of a parabola ? = ??2. The bead rotates in a circle of radius R when the wire is rotating about its vertical symmetry axis with angular velocity w. Find the value of c.

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2. Use the properties of the generating function F(q, P,t) = (q2 + P2 )cot wt - maqP csc wt 2 to derive: 2.1. the Kamiltonian N H = OF + V (q)+ OF 2m oq at where V(q) is the potential energy. 2.2. What would be the consequence(s) of defining this transformation such that the Kamiltonian is zero? 2.3. Use the transformation to find the equations of motion of the linear oscillator system H (q, p) = ( p2 + m?@-q2) 2m5. A head slides along a smooth wire bent in the shape of a parabola z = :72. The head rotates in a circle of radius R when the wire is rotating about its vertical symmetry axis with angular velocity w. Find the value of c