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A grandfather clock has a pendulum length of $1.0$ m and a bob of mass $m = 0.5$ kg. A mass of $2$ kg falls $0.7$ m in seven days to keep the amplitude of the pendulum oscillations steady at $0.03$ rad.
(a) The quality factor $Q$ of a damped oscillator is defined as
(1)What is the $Q$ of the system?
(b) With no energy input from the falling mass, the pendulum obeys the small angle equation of motion
(2)Find $\omega_0$ and $\beta$
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Answer
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Part (a), numerical answer should be $Q \sim 300$. Solution forgot to multiply by $2\pi$.
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