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    Lagrange of a simple pendulum

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    A pendulum consists of a mass m suspended by a massless spring with unextended length of b and spring constant k. Find Lagrange's equation of motion. Assume that the pendulum is constrained to swing in a single plane.

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    Following is the text part of the solution. Please see the attached file for complete solution. Equations, diagrams, graphs and special characters will not appear correctly here. Thank you for using Brainmass.

    Let the generalized coordinates be (r, θ).

    Kinetic Energy T= 1/2 m ( )
    Potential Energy V = 1/2 k (r-b)2 - mg ( r cos θ)

    Lagrange, L = T - V = 1/2 m ( ) - 1/2 k (r-b)2 + mg ( r cos θ)

    L = 1/2 m ( ) - 1/2 k (r-b)2 + mg ...

    Solution Summary

    Equation of motion for a simple pendulum was developed starting from the generalized coordinates. Two cases were discussed. First the case of a simple pendulum was analyzed. Then the case of a pendulum oscillating vertically was analyzed. Very detailed solution is provided in a 3-page word document. Please download this question/answer pair if you are interested in understanding how to solve classical mechanics problems using Lagrange method.