Do you have access to any scientific experiment which gives the period of a pendulum when the angle is 90°:
[![enter image description here][1]][1]

[this article](http://users.df.uba.ar/sgil/physics_paper_doc/papers_phys/mechan/Pendulo2.pdf) says T varies to about 18% up to 90°, so for a seconds pendulum the complete priod would be roughly 2.36. I d'like to know the ratio at 90° with a good approximation, and the span it can vary in relation to air friction, if the bob  is not massive. 

Also, I'd like to know the max speed of the bob at P0 and how it compares with the speed of same ball sliding without friction on a circular surface, would it be the same? 
[![enter image description here][2]][2]

What I am trying to understand here is rather complex, I'll try to explain:

If the block is placed on an air-track or other frictionless surface, the block would acquire a certain speed, momentum and KE in the opposite direction, right? same amount of momentum is lost by the bob and we can find speed loss. 

Isn't the same amount of speed lost by the bob when it is attached to a pendulum? Is this an important factor or may be the most importand factor (more relevant than air friction or friction at the pivot) for the increase of the period when the angle is greater than 30°? I figured out that this factor can account for about one third of the 18% increase, can you give a more accurate value?

What I am suggesting is that this (loss of horizontal momentum, which is made clear when the bob is not attached to a rod but slides on a block) is the most important factor that makes the actual period increase when the starting point deviates on the vertical direction.

  [1]: https://i.sstatic.net/8VEJI.png
  [2]: https://i.sstatic.net/sTqxq.png