Pendulum, find the damping constant of the air.

[hemetite]

Qn3

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?

 

[Quachama]

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).

:)

 

[thomate1]

Yes, your approach is correct and logical. The equation you used is the equation of motion for a damped harmonic oscillator, where b is the damping constant and m is the mass of the pendulum bob. By rearranging the equation and substituting the given values, you can solve for the damping constant of the air. However, it is always important to double check your calculations and make sure all units are consistent.