Undergrad How Do You Derive the Cosine of an Integral in Pendulum Motion?

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The discussion centers on deriving the cosine of an integral related to the motion of a simple pendulum using Lagrangian mechanics. Participants clarify the distinction between total and partial derivatives, emphasizing the importance of using the correct notation in physics. The conversation progresses to solving the Euler-Lagrange equation, leading to the correct formulation of the pendulum's motion, which includes recognizing the significance of signs in the equations. The final equations derived indicate the relationship between angular acceleration and displacement, highlighting the nature of restoring forces in oscillatory motion. The discussion concludes with a focus on understanding harmonic oscillators and the implications of the derived equations for various amplitudes.
  • #31
Oh, I think I figured it out on my own. I got ##\ddot θ ## in terms of the angular velocity, acceleration, and θ.
 

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