A weird oscillation

I thought this a few days ago.

$A$ is a pin which pinned on the wall.

The blue standard stick is positioned to a sufficiently place, to

Do oscillation as picture above, forever.

There are no friction force anyway, only gravity.

Is that true?

And if it is true, then how to calculate the period ?

#Mechanics

Easy Math Editor

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$