A small sphere 1 carrying charge (q_{1}) and having inertia (m_{1}) is constrained to moving inside a

Question:

A small sphere 1 carrying charge $q_{1}$ and having inertia $m_{1}$ is constrained to moving inside a narrow vertical tube (Figure P23.92). Fixed at the bottom of the tube is a small sphere 2 carrying charge $q_{2}$.

(a) Determine the equilibrium height $b$ for sphere 1 (ignore friction).

(b) Show that if sphere 1 is displaced from this equilibrium position by a small amount and then released, it moves in simple harmonic motion with angular frequency $\omega=(2 g / h)^{1 / 2}$.

Data from Figure P23.92

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