A uniform rigid bar of mass m and length L is suspended, in vertical plane, at...

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A uniform rigid bar of mass m and length L is suspended, in vertical plane, at point O by a string of length L. The horizontal force Facts at the rod's end, point A as shown. a) Using Lagrange's equations, write down the equations of motion of the rod for considerable values of 0₁ and 02. b) Assume small oscillations for 0₁ and 2 rewrite the equations of motion in matrix form (linearized equations) c) Using available symbolic manipulators (MATHEMATICA, or MATLAB), find the Natural frequencies and the corresponding mode shapes if m= 10 kg and L = 1 m. Hence, determine the response of the system due to assumed initial conditions and plot your results. wwwww L 02 G m, L A uniform rigid bar of mass m and length L is suspended, in vertical plane, at point O by a string of length L. The horizontal force Facts at the rod's end, point A as shown. a) Using Lagrange's equations, write down the equations of motion of the rod for considerable values of 0₁ and 02. b) Assume small oscillations for 0₁ and 2 rewrite the equations of motion in matrix form (linearized equations) c) Using available symbolic manipulators (MATHEMATICA, or MATLAB), find the Natural frequencies and the corresponding mode shapes if m= 10 kg and L = 1 m. Hence, determine the response of the system due to assumed initial conditions and plot your results. wwwww L 02 G m, L

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This question is asking for the analysis of a mechanical system that consists of a uniform rigid bar of mass m and length L which is suspended by a string of the same length L The system is subjected ... View the full answer