Lagrange's Equation Problem A hoop of mass M and radius R rest horizontally on a smooth table and one point on its circumference is now pinned to the table so that the hoop may swing freely about a vertical axis and a cute little bug of mass m crawls at constant speed vo about the circumference of the hoop. a) First, set up the equations of motion for this problem by choosing to view it as a system with two degrees of freedom with the force that the bug exerts against the hoop to be determined from the condition that the bug moves with constant speed. b) Second, set up the equations of motion for this problem by choosing to view it as a system with only one degree of freedom where the bug is constrained to be at a certain point on the ring at each instant of time. Show that the two formulations yield equivalent equations of motion for the hoop. Hint: Use conservation of angular momentum.