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6. Consider the double pulley system shown in the figure below. Use the coordinates indicated and determine the equations of motion. Pulley 1 X 4 - x Pulley 2 4 - 1 7. A particle moves in a plane under the influence of a force f = - Ard-1 directed toward the origin; A and a (> 0) are constants. Choose appropriate generalized coordinates, and let the potential energy be zero at the origin. Find the Lagrangian equations of motion. Is the angular momentum about the origin conserved? Is the total energy conserved? 8. Consider a vertical plane in a constant gravitational field. Let the origin of a coordinate system be located at some point in this plane. A particle of mass m moves in the vertical plane under the influence of gravity and under the influence of an additional force