- 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
Find the frequency of small oscillations of the bead about the
- 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!