### Lagrangian and Hamiltonian's Mechanics: Write down the Lagrangian L for two particles of equal mass m1 = m2 = m, confined to the x-axis and connected by a spring with potential energy U = ½ k x^2. (Here x is the extension of the spring, x = (x1- x2 -l), where l is the spring's outstretched length, and that mass l remains to the right of mass 2 at all times.] (b) Rewrite L in terms of the new variables X = ½(x1+x2) (the CM position) and x (the extension) and write down the two Lagrange equation of X and x (c) Solve for X(t) and x(t) and describe the motion.

Lagrangian and Hamiltonian's Mechanics: Write down the Lagrangian L for two particles of equal mass m1 = m2 = m, confined to the x-axis and connected by a spring with potential energy U = ½ k x^2. (Here x is the extension of the spring, x = (x1- x2 -l), where l is the spring's outstretched length, and that mass l remains to