First we find the minimum of the potential.
The second derivative of the potential is Plugging in and shows that is a local maximum and is a local minimum. So, we consider small oscillations about . Define . We would like to know the force on the particle as a function of . This can be easily found as follows: Since we are told to consider only small oscillations about the minimum, we can ignore that terms. The angular frequency of oscillations in the case where we have a spring with spring constant is , so, by analogy, the angular frequency of oscillations here is: Therefore, answer (D) is correct. |

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