When we swing, if a person stands on the swing without moving, the movement of the swing is similar to the movement of a single pendulum. When the swing from the lowest point to the highest point of the process, gravity does negative work, the kinetic energy of the system into the potential energy of the system, when the swing from the highest point back to the lowest point, the potential energy of the system into the kinetic energy of the system, the whole process of mechanical energy conservation, the swing will do equal amplitude swing.
If you want the swing to swing higher and higher, you must use external forces, their own swing, there is no way to use external forces, the system will not be able to obtain energy from the outside world. Only by swinging the person himself and the rope of the internal force work will be their own internal energy into the mechanical energy of the system, and the internal force work can only be achieved by the person on the swing standing up or squating down. But when the person swings to the balance position, the hands pull the rope, the rope to the same size as the reaction force to pull people.
This force overcomes the person's gravity to do work so that people suddenly stand up, people in this time the center of gravity will move up. The gravitational potential energy of the system increases. At this point, the tangential velocity has not changed that the kinetic energy has not changed, and the mechanical energy of the system increases. When the swing from the lowest point to the highest point in the process of slowly squatting, then in this process, gravity no longer does negative work, and nearly does not do work, and even does positive work. When the person rises to the highest point in the rapid stand-up. So that the gravitational potential energy increases. When the swing from the highest point swings back to the lowest point slowly squatting, so that its center of gravity is down, the position of the center of gravity falls, this process gravity is still doing positive work. Then in a cycle of gravity always do positive work. In this way, swinging people can convert their own internal energy into the mechanical energy of the swing.
In short, singing children's swings should be in the swing movement to the lowest point when the person quickly stands up, and then slowly squats, when the swing to the highest point, and then violently stand up, after the highest point and then slowly squat, to the lowest point and then violently stand up, later repeat the above action, that is, the higher the swing.