4. Two identical beads of mass m slide on a thin frictionless wire bent into a vertical circular hoop of radius R in the xz plane (with z vertical), centred on the origin. A light spring of spring constant k and unstretched length b is threaded onto the wire between the two beads, with the beads attached to the ends, so that the spring is bent into an arc subtending an angle b = b/R when unstretched. Describe the positions by the angles theta1 and theta2 from the origin, relative to the vertically downwards direction. Write out the lagrangian, and find the differential equations of motion. I am seriously lost when it comes to this question. I've tried writng the distance ftom the negative z axis, but I end up getting different combinations of beta, theta1 and theta2, at different points on the loop. Are the 2 angles from the x = 0 line?