The uniform garage door has a mass of 150 kg and is guided along smooth tracks at its ends. Lifting is done using the two springs, which are attached to the anchor bracket at A and to the counterbalance shaft at B and C. As the door is raised, the springs begin to unwind from the shaft, thereby assisting the lift. If each spring provides a torsional moment of M = (0.7θ) N · m, where θ is in radians, determine the angle θ₀ at which both the left-wound and right-wound spring should be attached at A so that the door is completely balanced by the springs, i.e., when the door is in the vertical position and is given a slight force upwards, the springs will lift the door along the side tracks to the horizontal plane with no final angular velocity. The elastic potential energy of a torsional spring is V_e = 1/2kθ², where M = kθ and in this case k = 0.7 N · m/rad. 

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3 m B A 4 m