The Lagrangian of a diatomic molecule is given by $$L = \frac{m}{2}\left( {\dot x_1^2 + \dot x_2^2} \right) - \frac{k}{2}{x_1}{x_2}$$ where, m is the mass of each atom and x1, x2 are displacements from equilibrium position and k > 0. The normal frequencies are
A. $$ \pm {\left( {\frac{k}{m}} \right)^{\frac{1}{2}}}$$
B. $$ \pm {\left( {\frac{k}{m}} \right)^{\frac{1}{4}}}$$
C. $$ \pm {\left( {\frac{k}{{2m}}} \right)^{\frac{1}{4}}}$$
D. $$ \pm {\left( {\frac{k}{{2m}}} \right)^{\frac{1}{2}}}$$
Answer: Option D
This Question Belongs to Engineering Physics >> Classical Mechanics
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