Consider the equations x a(θ-sin θ ) and z#a(1+cos0) where a is a constant. the z(x) curve is called a cycloid, and is the shape traced out by a point on the rim of a wheel that rolls on a flat surface. most often, both equations have a minus sign, which corresponds to the cusps (the "pointy corners') of the cycloid being at the bottom; however, we are interested in the upside-down version of the cycloid as described by the above form of the equations. consider a bead of mass m that slides without friction on a curved wire that follows one period of an "upside-down" cycloid. gravity acts along the z axis. (i) write down the lagrangian in terms of 0. (i) find the equation of motion (eom) for the bead. ) show that d2u/dt2+gu/4a -o, where u - cos( /2), leads to the same eom as obtained in part (i) above. (iv) show that the bead can oscillate, and that the motion in terms of 0, assuming we are not dealing with the limit of small oscillations, is not simple harmonic motion. (v) find the period for these oscillations