The uniform door has a mass of 20 kg and can be treated as a thin plate having the dimen...

The uniform door has a mass of 20 kg and can be treated as a thin plate having the dimensions shown. If it is connected to a torsional spring at A, which has a stiffness of k = 80 N • m/rad, determine the required initial twist of the spring in radians so that the door has an angular velocity of 12 rad/s when it closes at θ = 0° after being opened at θ = 90° and released from rest. Hint: For a torsional spring M = kθ when k is the stiffness and θ is the angle of twist.