Diatomic molecule as a linear harmonic oscillator

The diatomic molecule is an example of a linear hannonic oscillator provided that the interatomic force is an elastic one. Consider a molecule to be close to an isolated system. This signifies that two atoms of a molecule make oscillations relative to their CM, so that such oscillation can be reduced to an oscillation of a single body (with the mass equal to the reduced mass system) regarding the motionless fixed point nnder the action of the same interatomic force. 

For this case, we can write = m 2 (refer to Section 1.3.7). Considering the oscillations to be symmetrical, for any instant of time it is fair to say that 

Assume for the linear oscillator the interatomic force is an elastic one. This corresponds to the problem in harmonic approximation. Then, a force acts on any atom that is out of its equilibrium position  

Express in the first equation 2 through and in the second equation if j through 

Because + 2 where is the displacement of one atom relative to the other, we can write the expression for relative acceleration as, 2 = t Value m,m2l (m, + m2) is the reduced mass of the molecule, which is denoted by n (Section 1.3.9). Then the above equation corresponds to the harmonic oscillation of a single material point /x under the action of an elastic force - P  

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