A spherical pendulum consists of a bob of mass m attached to a weightless, extensionless rod of length l. The end of the rod opposite the bob pivots freely (in all directions) about some fixed point. Set up the Hamiltonian function in spherical coordinates. (If pϕ=0, the result is the same as that for the plane pendulum.) Combine the term that depends on pϕ with the ordinary potential energy term to define as effective potential V(θ,pϕ). Sketch V as a function of θ for several values of pϕ, including pϕ=0. Discuss the features of the motion, pointing out the differences between pϕ=0 and pϕ=0. Discuss the limiting case of the conical pendulum (θ= constant) with reference to the V-θ diagram.