# Pendulum Oscillation

1. Sep 27, 2009

### CaptainEvil

1. The problem statement, all variables and given/known data

A grandfather clock has a pendulum length of 0.7 m and a mass bob of 0.4 kg. A mass
of 2 kg falls 0.8 m in seven days, providing the energy necessary to keep the amplitude
(from equilibrium) of the pendulum oscillation steady at 0.03 rad. What is the Q of the
system?

2. Relevant equations

1) Q = $$\omega$$R/2$$\beta$$

2) Q = $$\omega$$0/$$\Delta$$$$\omega$$

3. The attempt at a solution

I figured only equation 1 would help me here, and I can re-arrange it as follows:

$$\beta$$ = b/2m (b = damping coefficient)

Then Q = m$$\omega$$R/b

when amplitude D is a maximum, we can differenciate wrt $$\omega$$ to obtain maximum (i.e $$\omega$$R)

$$\omega$$R = sqrt($$\omega$$20 - 2$$\beta$$2)

re-arranging yields

Q = m sqrt($$\omega$$20 - b2/2m2)/b

I'm kind of stuck because I don't know how to find the coefficient of damping b. Did I go in the wrong direction here? I know I have to use the information given about the pendulum dropping to find the flaw in the system, any help please?