The Pendulum Clock Escapement · AI Generator #GEN-9B74BD1C

Physics · mechanics

Problem

A grandfather clock uses a compound pendulum consisting of a thin uniform rod of length

L = 1.2\;\text{m}

and mass

m = 0.8\;\text{kg}

, with a solid brass disk of mass

M = 2.4\;\text{kg}

and radius

R = 0.15\;\text{m}

attached at the bottom end. The pendulum pivots about a point at the top of the rod. During normal operation, the escapement mechanism gives the pendulum a small impulse every swing to compensate for energy losses. However, when the clock stops, the pendulum continues to swing with decreasing amplitude due to air resistance and friction. If the pendulum is displaced to an initial angle

\theta_0 = 12°

and released from rest when the clock stops, find the period of small oscillations. Take

g = 9.8\;\text{m/s}^2

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