Genesis of the pendulum formula

[alba]

Can you give me a link where I can find a simple explanation of the formula of the period of a pendulum?

As far as I know, if the angle is 3°, the tension on the rope is g/ cos 3 and the horizontal T = 9,8 * tan 3 (0.0524) = 0.5 N. Is this the only force to consider?

Can you tell me how to proceed to find the time the bob reaches the vertical position? supposing l = .98 m , I know (from PE) that final v there is 16 cm/s and space traveled is 5.13 cm, but I cannot use the formula: t^2 = 2 s/a: since it is not an incline, a is not constant,

is integration the correct procedure?
of what function?
what is the formula for an arc?

Thanks, as I said, a link will do, how to find the exact value? how do we end up with √l/g?.

 

[DEvens]

You should be able to do this one for yourself with a few hints.

Don't forget that the tension in the rope has a direction. So it tends to pull the mass back towards the vertical orientation of the rope. So you need to work out what that force is as a function of angle. Then you need to take the approximation that the angle is very small, and use the small angle formula for trig functions. Then you should be able to recognize a simple harmonic oscillator.

https://en.wikipedia.org/wiki/Small-angle_approximation
https://en.wikipedia.org/wiki/Harmonic_oscillator