The uniform door has mass M and can be treated as a thin plate having the dimensions

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

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