Lagrangian Mechanics Example: The Compound Atwood Machine by Michel van Biezen (2017)
Source. Part of lagrangian mechanics lectures by Michel van Biezen (2017).The simplest harmonic oscillator system.
The period does depend on the initial height/angle, except for the very small angle approximation:
Pendulum Waves by Harvard Natural Sciences Lecture Demonstrations (2010)
Source. Holy crap.youtu.be/Ca7c5B7Js18?t=803 compares Lagrangian mechanics equation vs the direct x/y coordinate equation.
resonance in a mechanical system.
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