Write downthe Lagrangian L(xj, x 2 , i 1 , i 2 ) fortwoparticlesof equal masses. rnj = m2 = m, confined to the x axis and connected by a spring with potential energy U = !kx 2 • [Here x is the extension of the spring, x = (x 1 - x 2 - l), where l is the spring's unstretched length, and I assume that mass 1 remains to the right of mass 2 at all times.] Rewrite .C in terms of the new variables X = !(x 1 + x 2 ) (the CM position) and x (the extension), and write down the two Lagrange equations for X and x. (c) Solve for X (t) and x(t) and describe the motion.

Amass attached to a spring is displaced from its equilibrium position by 5cm and released. the system then oscillates in simple harmonic motion with a period of 1s. if that same mass–spring system is displaced from equilibrium by 10cm instead, what will its period be in this case? a mass attached to a spring is displaced from its equilibrium position by and released. the system then oscillates in simple harmonic motion with a period of . if that same mass–spring system is displaced from equilibrium by instead, what will its period be in this case? a) 0.5sb) 2sc) 1sd) 1.4s