A regulator clock is set so its pendulum swings either side of vertical

PHYSICS · Subjective · Fermi University Physics · Mechanics & Dynamical Systems · Oscillations and normal modes · Oscillations and normal modes

Modes, Packets and Media, Ch The anharmonic oscillator: frequency, harmonics and drift

Problem

A regulator clock is set so its pendulum swings

2.5^\circ

either side of vertical. A clockmaker widens the swing to

2.6^\circ

while adjusting the escapement. Using the series

T/T_0 = 1 + \theta_0^2/16

, find how many seconds a day the clock's rate changes because of this

0.1^\circ

increase in swing, and state whether the clock runs faster or slower.