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A molecule consists of two atoms whose centers are located at $\mathbf{r}_1$ and $\mathbf{r}_2$ respectively. The atoms are connected by a bond that can be approximated by a harmonic spring, so that its energy as a function of the separation between the atoms $\mathbf{r}=\mathbf{r}_1-\mathbf{r}_2$ is $$U(r) = \frac{akTr^2}{2}$$

Assuming that the molecule lives in one dimension, what will be the overdamped Langevin equation(s) for the motion of the molecule?

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What have you tried? You need to show your work, otherwise it will be a candidate for being closed. – DumpsterDoofus Feb 24 '14 at 17:43

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