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As shown in the figure, a loaded mine cart is being lifted by a frictionless pulley and a steel wire rope. Obtain the equations

 

As shown in the figure, a loaded mine cart is being lifted by a frictionless pulley and a steel wire rope. Obtain the equations of motion and natural frequency of vibration of the cart in the given position. Use effect of gravity in deriving the equations. The weight of the cart is 5,000g lb and modulus of elasticity of steel is Est = 30 x 106 lb/in. Pulley 30r Steel wire rope, 0.05" diameter Loaded mine cart

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