How Does a Cuckoo Clock Calculate Its Quality Factor and Battery Life?

[kraigandrews]

Homework Statement

Consider a small cuckoo clock in which the length of the pendulum is L, suspending a mass m with a period of oscillation T. The clock is powered by a falling weight (mass = M) which falls 2 m between the daily windings. The amplitude of the swing is 0.2 radians.
(A) Determine the quality factor Q of the clock.
Data: m = 54 g; T = 1.0 s; M = 949 g.

(B) How many days would the clock run if it were powered by a 1.5 volt battery with charge capacity equal to 1800 mAh

Homework Equations

T=2pi(L/g)^1/2

The Attempt at a Solution

E₀=(m+M)gL(1-cos$\Theta$)

I am unsure of how to find the amount of energy loss per cycle.
Or if the masses in the Energy equation are correct

 

[gneill]

The clock's falling weight does not participate in the pendulum motion -- it adds energy to the pendulum via a gear train and escapement mechanism.

How many "ticks" in a 24 hour period? How much energy is added by the falling weight in that time?