This system has 3 generalized coordinates : displacement of the spring , deflection angle of the (spring-)pendulum , and translation of the support.
Hence it's described by 3x 2nd order nonlinear ODE's and matlab has to solve 6x linearized 1st order ODE's .
Since the equations are rather complex , they're not stated here in this description. The .zip contains a .mp4 file of the animation.
Lucas Tassilo Scharbrodt (2021). spring pendulum with movable support - Lagrange Mechanics (https://www.mathworks.com/matlabcentral/fileexchange/67998-spring-pendulum-with-movable-support-lagrange-mechanics), MATLAB Central File Exchange. Retrieved .
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