What is the Q Factor and Resonance of a Simple Pendulum?

[physicsss]

I have no idea what the Q factor is in the following problem:

Consider a simple pendulum (point mass bob) 0.50 m long with a Q of 400.

How long does it take for the amplitude (assumed small) to decrease by two-thirds?

If the amplitude is 3.0 cm and the bob has mass 0.20 kg, what is the initial energy loss rate of the pendulum in watts? (The answer should have a negtive sign.)

If we are to stimultate resonance with a sinusoidal driving force, how close must the driving frequency be to the natural frequency of the pendulum?

 

[Tide]

Q is the "quality factor" and is a measure of the energy loss per cycle:

$$Q = \omega \left| \frac {E}{\Delta E} \right|$$

Low Q means high damping and high Q means low dampiing. You should be able to take it from there!

 

[physicsss]

How is the angular frequency related to amplitude and energy?

 

[Tide]

The angular frequency is related to the length of the pendulum:

$$\omega = \sqrt \frac {g}{L}$$

and the amplitude will look something like

$$x = x_0 \cos \omega t$$

from which you can calculate the velocity and kinetic energy (and you can also obtain the potential energy).