Question

A small cuckoo clock has a pendulum 25cm long with a mass of 10g and a period of 1s. the clock is powered by a 200gram weight which falls 2m between the daily windings. the amplitude of the swing is 0.2rad. what is the q value of the clock?

Answer 1

Q factor is defined as the ratio of the total amount of energy stored in the pendulum and total amount of energy lost per one cycle.

`Q=2\pi f (energy\ stored)/(power\ loss)`
We will need to figure out power loss and energy stored.
Power loss is happening due to friction. It is equal to power that the weight is supplying to the clock:

`P_l=(mg\Delta h)/(\Delta t)=(0.2\cdot 9.81 \cdot 2)/(24\cdot 60 \cdot 60)=0.000045W`
Now we need to figure out the energy stored in one the pendulum. We can think of this as potential energy of the pendulum:

`E_s=m_pgh_p=m_pgL(1-cos(\theta))=0.01\cdot 9.81 \cdot 0.25 \cdot (1-\cos(0.2))`

`E_s=0.0004888J`
Please see the attachment for clarification.
Now we can calculate the Q factor:

`Q=2\pi f (E_s)/(P_l)=2\pi (0.0004888)/(0.000045)=68.2`