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.
[tex]Q=2\pi f \frac{energy\ stored}{power\ loss}[/tex]
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:
[tex]P_l=\frac{mg\Delta h}{\Delta t}=\frac{0.2\cdot 9.81 \cdot 2}{24\cdot 60 \cdot 60}=0.000045W[/tex]
Now we need to figure out the energy stored in one the pendulum. We can think of this as potential energy of the pendulum:
[tex]E_s=m_pgh_p=m_pgL(1-cos(\theta))=0.01\cdot 9.81 \cdot 0.25 \cdot (1-\cos(0.2))[/tex]
[tex]E_s=0.0004888J[/tex]
Please see the attachment for clarification.
Now we can calculate the Q factor:
[tex]Q=2\pi f \frac{E_s}{P_l}=2\pi \frac{0.0004888}{0.000045}=68.2[/tex]
