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according to the definition of the Q-factor of damping, it is given by:

$Q = 2\pi\frac{Energy \; Stored}{ Energy \;Dissipated \; per \;cycle }$

Q = 1⁄2 --> Critical damping

Q > ​1⁄2 --> Over damped

Q < 1⁄2 --> Under damped

In my experiment, I am finding the condition for critical damping but when I calculate the Q factor I am getting very high values, even if the oscillations are underdamped. The data I am recording is the initial angle of the pendulum and the angle after 1 oscillation.

Is there any other formula to calculate the Q factor of damping in a pendulum based on the angle of the pendulum and Q factor.

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  • $\begingroup$ If your system is "underdamped" (it seems you observe oscillations), doesn't it mean that the energy dissipated is small compared to the energy stored. And thus, from your first definition, that Q>>1? $\endgroup$
    – user8736288
    Commented Sep 23, 2019 at 17:06

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You have the inequalities backward as related to the Q-factor. According to the definition you gave in the first equation, as the dissipation gets smaller, the Q-factor increases. If you are measuring an underdamped pendulum, the Q-factor should be large.

There is no simple way to calculate the Q-factor from dimensions of the pendulum, since the dissipation depends on energy loss due various contributions to friction, from the the pivot, motion through the air, etc.

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  • $\begingroup$ I am using a magnet and aluminium for the damping effect, still I am not getting anything close to 1/2 $\endgroup$
    – tmm
    Commented Sep 23, 2019 at 17:02
  • $\begingroup$ @ThaqibDamani2.0, You should have mentioned in your question that you are using eddy current to provide damping. If your pendulum is still underdamped, you need to increase the damping. $\endgroup$
    – amateurAstro
    Commented Sep 23, 2019 at 17:08
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    $\begingroup$ Thaquib, please note that for critical damping, the oscillation stops after only half of a single oscillation cycle. For overdamping, oscillations do not even occur. Everything else is underdamped. $\endgroup$
    – niels nielsen
    Commented Sep 23, 2019 at 18:05

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