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## Homework Statement

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?

## Homework Equations

1) Q = [tex]\omega[/tex]

_{R}/2[tex]\beta[/tex]

2) Q = [tex]\omega[/tex]

_{0}/[tex]\Delta[/tex][tex]\omega[/tex]

## The Attempt at a Solution

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

[tex]\beta[/tex] = b/2m (b = damping coefficient)

Then Q = m[tex]\omega[/tex]

_{R}/b

when amplitude D is a maximum, we can differenciate wrt [tex]\omega[/tex] to obtain maximum (i.e [tex]\omega[/tex]

_{R})

[tex]\omega[/tex]

_{R}= sqrt([tex]\omega[/tex]

^{2}

_{0}- 2[tex]\beta[/tex]

^{2})

re-arranging yields

Q = m sqrt([tex]\omega[/tex]

^{2}

_{0}- b

^{2}/2m

^{2})/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?