A vertical light rod of length l is pivoted at its top end. A small sphere of mass m and charge +q is attached to the bottom end of the rod. Another small sphere of charge −q is mounted a distance l directly above the pivot point. After a small disturbance, the rod swings back and forth in the vertical plane. Find the period of that motion.
Answer: The period T of the oscillation is see Eq. (6) below.
A first guess at the solution would be that for very small displacements, we could treat
the electrostatic force Fq0 as approximately
constant and vertical, opposite to the gravitational force mg. In that
case, the reduced gravitational acceleration g’ could be written as,
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