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- Homework Statement
- Oscillation of bead with gravitating masses:

A bead of mass m slides without friction on a smooth rod along

the x axis. The rod is equidistant between two spheres of mass M.

The spheres are located at x = 0, y = ± a as shown, and attract the

bead gravitationally.

Find the frequency of small oscillations of the bead about the

origin.

- Relevant Equations
- U = m * g * h

U = -g * m * M (1/r1 + 1/r2)

U = (-2 * g * m * M) / sqrt (a^2 + x^2)

The relevant equations has been me working out the gravitational potential energy. I was told to take the derivative twice from here, but I do not understand why. It leads into a taylor series expansion, which seems excessive, but I was not informed on any other way to do it. Any advice would be greatly appreciated!