Damping effect of swinging pendulum affect period?

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Lets say i have a magnetic pendulm, (basically a barmagnet suspended from a with a string tabletop) and a conductor at the bottom.

The conductor will ofcourse have Foucault currents generated in it, and this due to conservation of energy, will slow down the swinging of the pendulum, reducing the "amplitude" of its swing.

But my question is, will it also reduce the period it takes for the pendulum to oscillate?
Is the rate at which the amplitude decays, proportional to the decrease in speed so as to preserve the time taken?
 
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Let me answer this by asking another question.......When the conductor is present does the pendulum still move with S.H.M.?
 
Damping of a pendulum causes a (small) decrease in its frequency and thus the period increases. How much has to do with how much damping you apply.

What do you mean exactly when you say "Is the rate at which the amplitude decays, proportional to the decrease in speed so as to preserve the time taken?"