Q1. The motion of a swinging door with an adjustment screw that controls the amount of friction on the hinges is governed by the initial value problem 10" + be' + k0 = 0; 0(0) = 00, e'(0) = vo , where 0 is the angle that the door is open, I is the moment of onertia of the door about its hinges, b > 0 is a damping constant that varies with the amount of friction on the door, k > 0 is the spring constant associated with the swinging door, 0, is the initial angle that the door is opened, and vo is the initial angular velocity imparted to the door (see Figure). If I and k are fixed, determine for which values of b the door will not continuously swing back and forth when closing. Figure: Top View of Swinging Door

Q1. The motion of a swinging door with an adjustment screw that controls the amount of friction on the hinges is governed by the initial value problem 10" + be' + k0 = 0; 0(0) = 00, e'(0) = vo , where 0 is the angle that the door is open, I is the moment of onertia of the door about its hinges, b > 0 is a damping constant that varies with the amount of friction on the door, k > 0 is the spring constant associated with the swinging door, 0, is the initial angle that the door is opened, and vo is the initial angular velocity imparted to the door (see Figure). If I and k are fixed, determine for which values of b the door will not continuously swing back and forth when closing. Figure: Top View of Swinging Door