Spring Pendulum - Derivation (Fun with Lagrangians)

I love the spring pendulum because of its rich phase space views showing conservation of energy and the competing forces of gravity and spring stiffness. GlowScript = https://trinket.io/library/trinkets/f0dc9b4994 Jupyter (energy conservation looks like it's suffering from a numerical instability) = https://colab.research.google.com/drive/1WB-e4aoeFTCC9HtWBLsgC13HNFaj2BR6#scrollTo=HkXNsBpm1eUT You can support this channel once at https://account.venmo.com/u/letscodephysics or http://ko-fi.com/LetsCodePhysics, or monthly at http://patreon.com/LetsCodePhysics to help me release one additional video each month! Thank you, patrons! Fan Xinyu, Don Williams, Tripp Bishiop, Aaron Stevens, Jean-Manuel Izaret, Hugo Granström Subscribe for more videos! https://www.youtube.com/LetsCodePhysics?sub_confirmation=1 Discuss this video at http://reddit.com/r/letscodephysics, http://twitter.com/LetsCodePhysics https://pixabay.com/photos/slinky-spring-rainbow-colorful-4345888/ ReMix: Deltarune "Arcane Anticipation" By Saxxon Fox, http://ocremix.org This episode is brought to you in part by the University of North Florida Department of Physics