I work in an electric motor shop and we use overhead cranes to move the motors around the shop. When a crane moving a motor stops, the inertia and momentum of the motor causes the motor to continue moving. It now becomes a pendulum like object that swings back and forth. A method we use to dampen the swing is to try to move the crane in either direction right when the motor reaches the highest point in that direction. From a physics standpoint, why does this help to dampen the swing?

 

... When the crane stops abruptly, the crane and motor, in effect, develop counter clockwise angular momentum. By moving the crane in the opposite direction, a clockwise angular momentum is developed, which cancels the original.

 

The pendulum motion is damped because the tension in the cable gets relaxed by moving the crane toward the highest point of the swing where the load (motor) velocity is zero.

The weight of the motor is now free to fall straight down due to gravity. Then the tension in the cable is restored in the vertical direction and a small vertical oscillation results at a frequency proportional to the spring contant of the cable and the mass of the motor.

If the crane motion doesn't reach exactly above the motor, then some component of pendulum motion can occur but over a much smaller arc since the focal point was moved.

 

Anti-sway crane control is a classic exercise we give students to learn PID control.

 

At the peak of the swing, the motor has momentarily stopped in space.
If you then move the crane in the same direction so the crane is over the motor, there is no angular tension from the cable to pull the motor back from the top of the arc.
It will just drop vertically until the cable is taut.

There are also some Fuzzy Logic based controllers that do a good job of eliminating the swing of a crane load.

 

The design and controls of crane operation is a good explanation.
The operator of cranes in the more difficult load swing has a feel that some control engineers understand
which is operator designed physics. Grabbing an electrical engineering job sometimes has some unexpected challenges.
The technology has developed over time like electrical motors we have to learn how it's done by feel sometimes.