Question 2: (a) Using the positions of the two leftmost masses as generalized coordinates, find the La- grangian for this Atwood machine. (b) Find a coordinate transformation of the form x1 = x1(a, t) 12 = 12(a, t) 'LLLL with a a continuous parameter and x1 (0, t) = x1(t) x2(a, t) = 22(t) that leaves the Lagrangian invariant. Invoke the Noether The- orem to find the corresponding conserved quantity. 4m 2m