Is One Complete Cycle in a Damped Pendulum Theoretical?

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Kaneki123
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Okay...I just have a simple question...For a vibrating pendulum, a one complete cycle is considered when it displaces from a certain position A and then again returns to that certain position A...My question is that the damping is continuosly taking place on the pendulum, so there is no way that the pendulum is returning exactly at that same point, so is there a problem in my assumption or "one complete cylce or one complete vibration" is all theoretical?
 
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You appear to have some misconception about a "full cycle." Imagine that we begin to measure the cycle from the vertical, and the pendulum first swings to the left, then back to the center, then to the right, and finally back to the center. A full cycle takes in all the motion just described. Your description sounded more like a half cycle.

Regarding damping, and again starting from the vertical, the pendulum swings left, then back to center, then to the right, then back to center, and all of this remains true, with, or without, damping. It passes repeatedly through the center, so it most definitely returns to that point.
 
Technically speaking, there is no complete cycle for a dampened oscillation if your definition for a cycle requires that the system returns to its original state. However, there is an amplitude that decreases with time and a period of oscillation between minimum or maximum displacement.

AM