10-15% Off all my Merch :) Use Code 42069 over on https://papaflammy.myteespring.co/ 10% or more Off ALL Face Masks! =D https://stemerch.com/collections/face-masks Pendulum Differential Eq: https://youtu.be/efvT2iUSjaA Series of Elliptic: https://youtu.be/TC-6o9MmJgk Advent Calendar Playlist: https://www.youtube.com/playlist?list=PLN2B6ZNu6xmfKpqyNztnGbyyQ7QbGEH6M Try Wondershare Document Cloud right now :) https://bit.ly/3fj1Xnj Subscribe to Document Cloud at 50% off! https://bit.ly/3fj2aa5 Today we are going to calculate the solution to the nonlinear pendulum differential equation, its period time for certain initial displacements, gravitational acceleration and string length. We implement the complete elliptic integral of the first kind into python and approximate the period time to a certain degree. Enjoy :) Video sponsored by Wondershare btw! =) ------------------------------------ The Code: import math def elliptic(n,k): k = math.sin(k *math.pi / 360) s = 1 for i in range(0, n+1): p = 1 for j in range(1, 2*i+1+1 , 2): p *= j / (j+1) s += (p * k**(i+1))**2 return float(math.pi/2 * s) l = int(input("String length l? ")) g = float(input("Gravitational acceleration g? ")) phi = float(input("Initial displacement phi_0? ")) n = int(input("Degree of approximation n? ")) print('') print("Period time T =", 4*math.sqrt(l/g)*elliptic(n, phi)) ----------------------------------------------------- Help me create more free content! =) https://stemerch.com/ https://www.patreon.com/mathable https://papaflammy.myteespring.co/ Merch :v - https://papaflammy.myteespring.co/ https://www.amazon.com/shop/flammablemaths https://shop.spreadshirt.de/papaflammy Become a Member of the Flammily! :0 https://www.youtube.com/channel/UCtAIs1VCQrymlAnw3mGonhw/join 2nd Channel: https://www.youtube.com/channel/UCnyZe3jFb27omDvOlR5BhZA -------------------------------------------------------------------------------- Wanna send me some stuff? lel: Postfach 11 15 06731 Bitterfeld-Wolfen Saxony-Anhalt Germany -------------------------------------------------------------------------------- Twitter: https://twitter.com/FlammableMaths Instagram: https://www.instagram.com/uncomfortably_cursed_mathmemes/ Flammy's subreddit: https://www.reddit.com/r/FlammyBois Facebook: https://www.facebook.com/flammablemaths/ Want to know more about me? Watch my QnA! =D https://youtu.be/IjCWSDBI9Zc ... https://www.youtube.com/watch?v=jN9-AoAZgR8

Leibniz Rule: https://youtu.be/wkh1Y7R1sOw Coxeter's Integral: https://youtu.be/1FixkRTDem0 Gauß' Multiplication Formula: https://youtu.be/Z9FpJcHqURs Arctan Integral: https://youtu.be/_zqHrFKJsFY Today we derive a wonderful expression for the integral from 0 to infinity of sin(xt)/te^(-zt). We will make use of the Leibniz Rule for integration / Feynman Integration to get a final expression in terms of the arctan. Enjoy this beauty! =D Help me create more free content! =) https://www.patreon.com/mathable Merch :v - https://papaflammy.myteespring.co/ https://www.amazon.com/shop/flammablemaths https://shop.spreadshirt.de/papaflammy Become a Member of the Flammily! :0 https://www.youtube.com/channel/UCtAIs1VCQrymlAnw3mGonhw/join 2nd Channel: https://www.youtube.com/channel/UCnyZe3jFb27omDvOlR5BhZA -------------------------------------------------------------------------------- Wanna send me some stuff? lel: Postfach 11 15 06731 Bitterfeld-Wolfen Saxony-Anhalt Germany -------------------------------------------------------------------------------- My Website: https://papaflammy.engineer/ Instagram: https://www.instagram.com/uncomfortably_cursed_mathmemes/ Flammy's subreddit: https://www.reddit.com/r/FlammyBois Twitter: https://twitter.com/FlammableMaths Facebook: https://www.facebook.com/flammablemaths/ Got some time to spare? Make sure to add captions to my videos! =) http://www.youtube.com/timedtext_cs_panel?c=UCtAIs1VCQrymlAnw3mGonhw&tab=2 Want to know more about me? Watch my QnA! =D https://youtu.be/IjCWSDBI9Zc ... https://www.youtube.com/watch?v=OuIfkX18IQg