Swinging Door. The motion of a swinging door with an adjustment screw that controls...

Swinging Door. 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 Where θ is the angle that the door is open, I is the moment of inertia 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,θ₀ is the initial angle that the door is opened, and V₀ is the initial angular velocity imparted to the door (see Figure 4.10). If I and k are fixed, determine for which values of b the door will not continually swing back and forth when closing.