A small (point) mass m, which carries a charge q, is constrained to move vertically inside a narrow, frictionless cylinder (Figure). At the bottom of the cylinder is a point mass of charge Q having the same sign as q.

(a) Show that the mass m?will be in equilibrium at a height y₀ = (kqQ/mg)^1/2.

(b) Show that if the mass m?is displaced by a small amount from its equilibrium position and released, it will exhibit simple harmonic motion with angular frequency ??= (2g/y₀)^1/2.

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