6. Circular reasoning Two identical masses m are constrained to move on a horizontal hoop. Two identical springs with spring constant k connect the masses and wrap around the hoop as seen in the figure to the right. (a) Please produce the differential equations of motion for this system. You may wish to use the position of each mass on the hoop, x, relative to it's equilibrium position as your two coordinates. You may (or may not...) find it easier to use summation of Newtonian forces than the Lagrangian. (b) Find the normal modes and their frequencies, and describe (in words and/ or diagrams) the motion of the masses when the system is in each of the normal modes