Two identical atoms in a diatomic molecule vibrate as harmonic oscillators. However, their center of mass, midway between 1hem, remains at rest.
(a) Show that at any instant, the moment of the atoms relative to the center of mass are p and -po (b) Show the total kinetic energy K of the two atoms at any instant is the same as that of a single object with mass m/2 with a momentum of magnitude p. (Use K = p2/2m.) This result shows why m/2 should be used in the expression for f in Example 13.7 (Section 13.4).
(c) If1he atoms are not identical but have masses m, and m2, show littlie result of part (a) still holds and the single object’s mass in part (b) is m, mzI(m, + m2)’ The quantity m, mJ (m, + m2) is called the reduced mass of the system.