Why does a gyrocompass need to respond correctly to a ship’s acceleration?

A gyrocompass relies on pendulosity to establish its north-seeking property, which allows it to function by responding to the force of gravity. However, because this mechanism is sensitive to gravity, it also inevitably responds to vehicle [accelerations].123

If a gyrocompass did not account for these accelerations, the torques generated by north-south movements would cause the instrument to wander, rendering it useless for navigation. To maintain accuracy, the system must be designed so that its period of oscillation is tuned to a specific value—known as the Schuler period—which ensures that the precession of the gyroscope spin-axis caused by acceleration matches the rate of change of the angle between the true and apparent meridians seen from a moving vehicle. By correctly responding to and compensating for these accelerations, the gyrocompass can accurately indicate true north even while the ship is in motion.3