Why must the oscillation of a gyrocompass be damped?

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A gyrocompass must be damped so that it can settle on the meridian rather than continuously passing through it.1

Without damping, the spin axis of a gyrocompass traces an elliptical path about the meridian and the horizontal, causing the instrument to oscillate indefinitely. Damping is the process of changing the system's energy state by opposing the velocity of the gyroscopic element. By applying specific torques—such as those generated by the restricted flow of a viscous fluid or through a servomechanism—the elliptical motion is converted into a spiraling-in motion that allows the unit to stabilize at true north.1