More Words, Deeper Hole

Is a swing really a second law demonstration? I thought it had more to do with balance and changing the center of mass of the pendulum(swinger).

Thought experiment: The observer is watching a swinger from the side. The swinger is facing left. The swinger is sitting motionless directly below the bar. The swinger's feet are tucked up under the swing with heels near buttocks. This puts the swingers center of mass at about her hips. The whole system is at equalibrium.

The swinger then extends her legs straight out. (To the left from the point of view of the observer.) This moves her center of mass to the observer's left, no longer directly below the bar. The off center mass falls back toward the center, causing the swinger's body to move backward. Momentum causing the center of mass to pass the equilibrium point and swing the same distance to the right as the moved center of mass was to the left.

If the swinger freezes her posture, then barring any friction, she should continue this small oscillation forever. Instead, at the top of her right ward swing, she tucks her legs up under herself, this pulls the CoM to a point beyond the top point of the unaided swing. This adds potential kinetic energy to the swing and she drops through the equilibrium point even faster, Swinging higher on the left. Where she can extend her legs again and add yet more momentum to the system.


(All this assumes a swinger who can hold her torso perfectly rigid. I know that typically a swinger extends legs on the down swing, and tucks on the backswing, but when she does this she is also shifting her torso backwards, leaning back on the chains and shifting her CoM in that direction. So everything above is actually backward.)