The carriage of mass 2m is free to roll along the horizontal rails and carries the two spheres, each of mass m, mounted on rods of length l and negligible mass. The shaft to which the rods are secured is mounted in the carriage and is free to rotate. If the system is released from rest with the rods in the vertical position where θ = 0, determine the velocity v_x of the carriage and the angular velocity θ˙ of the rods for the instant when θ = 180°. Treat the carriage and the spheres as particles and neglect any friction.

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m m 1, 2m