Attwood's machine A uniform circular pulley of mass 2m can rotate freely about its axis of symmetry which is fixed in a horizontal position. Two masses m, 3m are connected by a light inextensible string which passes over the pulley without slipping. The whole system undergoes planar motion with the masses moving vertically. Take the rotation angle of the pulley as generalised coordinate and obtain Lagrange's equation for the motion. Deduce the upward acceleration of the mass m.