3. A bead of mass m is threaded on a frictionless wire that is bent into a helix with cylin- drical polar coordinates (p, ø, z) satisfying z The z axis points vertically up and gravity vertically down. co and p = R, with c and R constants (a) as a function of and its conjugate momentumpo. (b) Using as your generalized coordinate, write down the Hamiltonian H Write down the Hamilton's equations and solve for ø and hence z.

3. A bead of mass m is threaded on a frictionless wire that is bent into a helix with cylin- drical polar coordinates (p, ø, z) satisfying z The z axis points vertically up and gravity vertically down. co and p = R, with c and R constants (a) as a function of and its conjugate momentumpo. (b) Using as your generalized coordinate, write down the Hamiltonian H Write down the Hamilton's equations and solve for ø and hence z.