The Simple Pendulum with the Period Corrected

Note: at 12:20 a slight mistake is made, it should be sqrt(2sin^2(theta0/2) - 2sin^2(theta/2)) in the denominator. This error carries on, but then I take the ready-simplified form later, which saves it.
Some of the properties of the basic pendulum are covered, namely the period. Though quite basic, it is a good refresher. Then a correction for larger angles of the pendulum are derived. Also, back to the white screen today!

[@kushalthaman3110]

Ah this is Morin 4.23 right? The final integral is an elliptic integral of the first kind so it would be cool if you show the even more general form there.

[@SlippingHexagons]

Yes it is :D Ok, thanks for the suggestion!

[@tujan7598]

Nice job! Who needs approximations?

[@SlippingHexagons]

Haha :) Though there were approximations here cuz the full answer is an infinite series, see Kushal's comment below :D

[@tujan7598]

5:00, isn't it theta^3? (if you consider the taylor series for sin(x))

[@SlippingHexagons]

Yes, that's right. This was back when I did videos in one take I think 😅

[@tujan7598]

11:52 :(

[@SlippingHexagons]

haha :P