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Beyond the fact that I can't find any data with enough information to make any use of, it seems to me that you are barking up the wrong tree to try to relate the period change to an amplitude change that depends on where in the cycle you add the quarters. (If I read correctly between the lines, you seem to be treating this as an inelastic collision between the pendulum and initially motionless quarters with an energy loss occurring if the pendulum happens to be moving.)
First of all, the drive mechanism will presumably act to counter any amplitude change that might result from whatever mechanical disturbance might occur during the quarter placement.
Second, the period change from adding quarters will likely have more to do with the change in the relative mass distribution (e.g. altering the radius of gyration) than any change in amplitude.
John Mallinckrodt
Cal Poly Pomona