Pendulum, find the damping constant of the air.

AI Thread Summary
To find the damping constant of air for a pendulum with a length of 1m and a bob mass of 50g, the displacement formula x = A * exp(-bt/2m) is used. The initial amplitude is 15 degrees, and after 1000 seconds, it reduces to 5.5 degrees. By substituting these values into the equation, the relationship 5.5/15 = exp(-b10000) is established. The method is confirmed as correct, having been applied successfully to a similar problem previously. The calculated damping constant b is essential for understanding the effects of air resistance on pendulum motion.
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A pendulum length of 1m has a bob which has a mass of 50g. It is released from an initial angle of 15degrees. After 1000s, its amplitude is reduced by the damping force of the air to 5.5degrees. What is the value of the damping constant of the air?

Ans.
I need to check whether what i am doing is correct.

the displacement of the pendulum bob will be given by

x= A * exp(-bt/2m)

where A is the amplitude.

i just put all the value in

5.5 = 15 * exp(-b1000/2*0.05)

5.5/15 = exp(-b10000)

the value b will be damping constant of the air...

correct and logical?
 
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Yes, I used that method for a very similar textbook problem (the only difference mass was not given and the question asked for b/2m) and got the right answer (.001).

:)
 

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