Lock-in effect (physics)

The lock-in effect is the mutual influence of weakly coupled oscillators .

First observation

The lock-in effect was probably first observed by Christiaan Huygens . In his book Horologium Oscillatorium , published in 1673 , he reports a strange phenomenon that he observed in pendulum clocks.

Was used for navigation on ships gimbal suspended pendulum clocks . In the event that a watch should fail, you usually have two identical watches with you. Huygens now observed that two clocks on such a ship were not only about the same in terms of their precision, but also exactly the same. They always ticked at the same moment. Even if the correspondence was intentionally disturbed, the pendulums would synchronize again in a short time, in this case the pendulums moved in push-pull (out of phase, mirror symmetry).

This phenomenon only occurred when the clocks were both set precisely. If one clock ran significantly faster than the other, they did not agree.

Huygens' interpretation was that a vibration was transmitted via the bar on which both clocks were hung. However, the movement of the beam was so small that it was not visible.

This effect was also observed in observatories on their high-precision pendulum clocks when they were hung on the same wall. After rotating the vertical axis of a clock by 90 degrees, this spontaneous synchronization no longer occurred.

general description

With a frequency difference between uncoupled oscillators below the lock-in threshold , the lock-in effect means that both oscillate at the same frequency when they are coupled. The lock-in threshold depends on the strength of the coupling. If the frequency difference is greater than the lock-in threshold, the coupling of the oscillators leads to a reduction in the difference frequency.

This effect occurs not only with mechanical, but also with all other vibrations. Electric oscillating circuits and laser resonators also show this phenomenon. With the laser gyro in particular , the accuracy is essentially limited by the lock-in effect.

The frequency difference of weakly coupled oscillators is

${\displaystyle \Delta f={\sqrt {f_{0}^{2}-f_{L}^{2}}}}$

where stands for the frequency difference without coupling and for the lock-in threshold. ${\displaystyle f_{0}}$ ${\displaystyle f_{L}}$

literature

• C. Huygens: The pendulum clock - Horologium Oscillatorium, Ed .: A. Heckscher, A. v. Oettingen, Verlag von Wilhelm Engelmann, Leipzig (1913) p. 24.
• R. Rodloff: Does the optical super gyro exist ?, Z. Flugwiss. Space exploration 18 , 2-15 Springer-Verlag (1994).