Double Attwood machine A light pulley can rotate freely about its axis of symmetry which is fixed in a horizontal position. A light inextensible string passes over the pulley. At one end the string carries a mass 4m, while the other end supports a second light pulley.
A second string passes over this pulley and carries masses m and 4m at its ends. The whole system undergoes planar motion with the masses moving vertically. Find Lagrange's equations and deduce the acceleration of each of the masses.