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This question already has an answer here:

Does air resistance increase or decrease the period of a simple pendulum?

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marked as duplicate by John Rennie newtonian-mechanics Jun 15 at 9:32

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  • $\begingroup$ A simple search gives : scirp.org/journal/PaperInformation.aspx?PaperID=73856 $\endgroup$ – Solar Mike Jun 15 at 8:22
  • $\begingroup$ How can you define a period for a motion which is not periodic? $\endgroup$ – eranreches Jun 15 at 8:47
  • $\begingroup$ @eranreches For damped simple harmonic motion where the displacement is $x = Ae^{-\beta t}\cos \omega t$, the period is defined to be $2\pi/\omega$. This corresponds to a "common sense" idea of the period if the damping is small, and is consistent with the definition when $\beta = 0$. $\endgroup$ – alephzero Jun 15 at 9:08
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You can see that air resistance increases the period by a common-sense argument, without doing any maths.

Suppose the mass is at its maximum position, and moves to the central position in time $t$. If there is air resistance, the speed of movement of the mass will be less because the air resistance slows it down, and therefore $t$ will be larger.

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