Find a general solution
The general solution of the given equation is .
The differential equation is
Then the auxiliary equation is
The roots of the auxiliary equation are:
Therefore, the general solution is:
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 is the angle that the door is open, is the moment of inertia of the door about its hinges, is a damping constant that varies with the amount of friction on the door, is the spring constant associated with the swinging door, is the initial angle that the door is opened, and is the initial angular velocity imparted to the door (see figure). If and are fixed, determine for which values of the door will not continually swing back and forth when closing.
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