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.

Given: M = 20 kg k = 80 @ = 12 N-m rad rad P = ON S a = 0.8 m b = 0.1 m c = 2 m