A cart of mass 2m rolls on a horizontal surface without friction. The cart is connected...

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A cart of mass 2m rolls on a horizontal surface without friction. The cart is connected to a rigid wall by a spring of stiffness k. A disc of radius R and mass m rolls on the cart without slipping. The centre of the disc is connected to a rigid wall by a spring of stiffness 2k. The coordinate x1 describes the horizontal displacement of the cart from the equilibrium position. The coordinate x2 describes the horizontal displacement of the centre of the disc from the equilibrium position. The coordinate 0 describes the angular rotation of the disc in the clockwise direction. Derive the two coupled equations of motion of the system using the Lagrange Equations. Use x1 and x2 as your generalized coordinates. 2k www k ww R 2m X2 m |> XI 10 www A cart of mass 2m rolls on a horizontal surface without friction. The cart is connected to a rigid wall by a spring of stiffness k. A disc of radius R and mass m rolls on the cart without slipping. The centre of the disc is connected to a rigid wall by a spring of stiffness 2k. The coordinate x1 describes the horizontal displacement of the cart from the equilibrium position. The coordinate x2 describes the horizontal displacement of the centre of the disc from the equilibrium position. The coordinate 0 describes the angular rotation of the disc in the clockwise direction. Derive the two coupled equations of motion of the system using the Lagrange Equations. Use x1 and x2 as your generalized coordinates. 2k www k ww R 2m X2 m |> XI 10 www

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To derive the equations of motion for the system using the Lagrange equations we need to start by defining the kinetic and potential energy of the system in terms of the generalized coordinates x1 and ... View the full answer