Exact Solution of the Nonlinear Pendulum [No Approximations, engis gtfo]

Still looking for the perfect Christmas present? :) Why not try out Brilliant this year? =D https://brilliant.org/FlammableMaths Elliptic Integral Series Expansion:    • Complete Elliptic Integral of the 1st Kind...   Physics Playlist:    • Newtonian mechanics: Rope sliding down a t...   Today we solve the equation of motion of a free undamped pendulum EXACTLY without small angle approximations. We reduce the order of the nonlinear second order differential equation and proceed to integrate like madlads. We finally arrive at an expression for the period time in terms of the Complete Elliptic Integral of the 1st Kind! :D Enjoy :3 Video sponsored by Brilliant btw! :) Help me create more free content! =) https://stemerch.com/   / mathable   Merch :v - https://papaflammy.myteespring.co/ https://www.amazon.com/shop/flammable... https://shop.spreadshirt.de/papaflammy Become a Member of the Flammily! :0    / @papaflammy69   2nd Channel:    / @npcooking69   -------------------------------------------------------------------------------- Wanna send me some stuff? lel: Postfach 11 15 06731 Bitterfeld-Wolfen Saxony-Anhalt Germany -------------------------------------------------------------------------------- Twitter:   / flammablemaths   Instagram:   / uncomfortably_cursed_mathmemes   Flammy's subreddit:   / flammybois   Facebook:   / flammablemaths   Want to know more about me? Watch my QnA! =D    • Question and Answer Time with Papa Flammy ...