Q1. The motion of a swinging door with an adjustment screw that controls the amount offriction on the hinges is governed by the initial value problem10" + b0' + k0 = 0;0(0) = 00,O'(0) = vo ,where 0 is the angle that the door is open, I is the moment of onertia of the door about itshinges, b > 0 is a damping constant that varies with the amount of friction on the door, k > 0is the spring constant associated with the swinging door, 0, is the initial angle that the door isopened, and vo is the initial angular velocity imparted to the door (see Figure). If I and k arefixed, determine for which values of b the door will not continuously swing back and forthwhen closing.Figure: Top View of Swinging Door

Solution: As per the given data,

Answered: Q1. The motion of a swinging door with…

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