Have you ever been to a catholic mass? When it comes time for communion, everyone lines up to recieve it from one of several distrubutors. The distributor says “body of christ” and offers you the little wafer; you respond “amen,” put it in your mouth, make the sign of the cross, and move on. In every communion line I have been in or witnessed, people slowly shift their weight from left to right as they waddle their way down to the distributor guy.
This situation could be modeled as an odd form of a driven oscillator. The period of time it takes to give a single person the communion wafer is the variable that encapsulates the behavior of the system. If the period were really small and each person only took 0.1 seconds to recieve communion, there’d be no waddling – people would just walk straight through the line, get their wafer and go. If the period were really long, say 30 seconds, the line would move more like something at an amusment park or fast food operation – you’d move a bit, then sit and wait a bit. With a period on the order of 5 seconds, you get the waddling behavior.
Why does the waddling happen when the line moves at only certain speeds? The answer is minimization of energy; moving continuosly takes a lot less energy than repeatedly starting and stopping. When you walk at a comfortable pace, your feet (and therefore your body) are constantly in motion and you don’t realize much of a benefit, energetically speaking, from waddling back and worth. When you’re moving slower, however, you waste a bunch of energy by moving a bit and then stopping. By shifting your weight from left to right, you’re just bouncing your momentum back and forth instead of starting and stopping it. This is the same reason large people tend to have more of a waddle in their walks; because they’re bigger, the energy saved by waddling instead of stopping and starting again persists to higher velocities than for regularly sized people.
Just something to think about.