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2) The dynamic system in the figure operates on a vertical plane and a horizontal guide. A spring with constant kis connected to a fixed wall and a block with mass me the spring is unstretched when x = 0. The block moves within the horizontal guide, which is smooth. Attached to the center of the block is a simple pendulum which swings about a smooth hinge in the center of the block. The mass of the rod of the pendulum is negligible in comparison to the mass mz of the sphere at the end of the pendulum. Using Lagrangian mechanics, determine the equations of motion of this dynamic system and express them as a first order system prostor