Use the Hamiltonian method to find the equation of motion of a particle of mass m constrained to move on the surface of a cylinder defined by x2+y 2=R2 .The particle is subject to a force directed toward the origin and proportional to the distance of the particle from the origin F= -kr

Problem 4: Starting from the origin at time t = 0, a particle is given an initial velocity vo along the +x axis. The particle's motion can be described by v(x) = vo(1kx)¹/3 where k is a positive constant. (a) Determine the retarding force F(v) as a function of velocity. [Note: Don't write your final answer in the form F(x, v)! You know v(r), so make sure your expression contains no explicit dependence on z.] (b) Determine x(t), the position of the particle as a function of time. (c) Find the time and place where the particle comes instantaneously to rest, tƒ and xƒ. For each part, check your result for dimensional consistency and limiting-case behavior.