The door will close automatically using torsional springs mounted on the hinges. Each spring has a stiffness k = 50 N • m/rad so that the torque on each hinge is M = (50θ) N • m, where θ is measured in radians. If the door is released from rest when it is open at θ = 90°, determine its angular velocity at the instant θ = 0°. For the calculation, treat the door as a thin plate having a mass of 70 kg.

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