Damped Pendulum, finding Q factor

m0nk3y

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

A pendulum has a period of 5seconds. It is damped so that the amplitude falls to one half its original value in 100seconds. What is the Q?

I am having trouble relating the Q with the information I have.

Period = 5 seconds
There are 5 periods
ω = 2π/5



Please help!

Thanks XD

2. Relevant equations



3. The attempt at a solution
I tried getting the total Energy E= T+V but then I have no idea what to do with that to get the Q.

dwintz02

Use Q = w*(Energy)/(Power Loss)

I'd stay away from calculating the total energy. Instead, think about how you can relate your givens (amplitude and amplitude loss) to energy and power loss. Does this help?

m0nk3y

Thanks for your reply.

I have seen that equation before, but I don't know what is my power loss. Since the amplitude is decreasing, I know that the amount it is decreasing by in respect to time should be somehow related to the power lost but I still don't know howto do that.

dwintz02

In this case, think of power loss as energy loss per unit time. Focus on finding the relationship between energy and amplitude(it's a simple proportion and is probably in your book). Once you find that relation, you can relate the power loss to the amplitude loss per unit time, which is given.