Determine the required conditions for stable equilibrium

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Reference no: EM131465162

Question: The cart shown in Figure is attached to the wall by a spring of stiffness k. As shown, the spring is undeflected. The pendulum is attached to the cart by a frictionless pin and a torsional spring of stiffness kθ. The following data set applies: mc = 5 kg, mp = 1 kg, L = 0.5 m, kθ = 3.5 N m/rad, k = 200 N/m. Tasks:

(a) Select coordinates and draw the free-body diagram for each body.

(b) Obtain the EOMs for the system using Newtonian principles. Present in matrix format. Apply small-angle assumption.

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(d) Obtain the eigenvalues and normalized eigenvectors for the system.

(e) State the uncoupled modal equations of motion and the transformation from modal to physical coordinates.

Reference no: EM131465162

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