Why Does a Pendulum's Motion Change Direction Over Time?

[Josh Wilson]

Occasionally while eating at restaurants, I will swing the lamp hanging above the table and observe its motion. One feature has puzzled me for some time: at first the light swings back and forth linearly in the plane of motion corresponding to the initial release point. However, after some time the pendulum (light) changes its motion so as to swing sometimes in a circular fashion, and sometimes in a linear fashion whose direction is different than the initial direction. The direction and type of motion seem to be constantly changing.

Is this a feature of pendulums in general, or is there some complexity due to the fact that the light is not a simple point mass?

 

[Danger]

Welcome to PF, Josh.
I'm the least educated person here, so I can give you only my initial thought as opposed to something solid. My first thought is that the motion probably has more to do with the suspension system (chain, electrical cord, rods, etc.) than with the lamp itself. That's probably wrong, but the first thing that comes to mind.

 

[Josh Wilson]

You may be right. I suspect there is some coupling to higher order oscillation modes which causes the pendulum direction to slowly change over time - though these modes must be too small to actually see. Initially, I thought it might be some kind of Foucault pendulum effect, but then the oscillation would only change direction once per day...

 

[Cleonis]

The cord of the lamp will not be equally elastic in all directions. Or maybe for some direction of swing the effective cord length is longest in one particular direction of swing, and shortest in the perpendicular direction. And period of swing depends on cord length.

Probably those two directions already have names, but I can't remember. I'll just make up new names. 'Major swing' and 'minor swing' for the two directions described above.


When you start a lamp swinging you can think of its initial swing as a composition of partly major swing and partly minor swing. As described, the major swing and the minor swing don't have the same period. As a consequence, what is initially a linear swing opens up, changing into motion along an ellipse.

This effect is one of the reasons that building a Foucault pendulum setup is very hard. Additional measures are necessary to keep the plane of swing from opening up.

 

[PJC01]

This is an interesting observation and it is not uncommon for pendulums to exhibit changing directions of motion. This phenomenon is known as "chaotic motion" and it is a feature of many physical systems, including pendulums.

The reason for this behavior is due to the complex interplay between various forces acting on the pendulum, such as gravity, friction, and air resistance. These forces can cause small variations in the motion of the pendulum, leading to a chaotic and unpredictable path.

In addition, the fact that the light is not a simple point mass may also contribute to the changing direction of motion. The weight distribution and shape of the light can affect the pendulum's center of mass and alter its motion.

Overall, the changing direction and type of motion in pendulums is a result of the intricate dynamics of the system. It is a fascinating aspect of physics and highlights the complexity of even seemingly simple systems.