By Meredith Barthold
In this video the metronomes communicate with one another once they are on a moving surface, and not a static surface. Since they are on the same moving surface they are connected to one another. What is happening is the surface is absorbing the motion to create a group effect to each oscillator. Due to the fact that they are moving together, the differences in oscillations eventually have to stop and begin to move as one.
So since the actual physics behind this is more advanced than what is covered in this class, I am comparing the metronomes and the oscillators to springs that are attached to each other. If there is a force put on one of the springs, there will be a restoring force that occurs all the way through the line of springs, no matter how many springs there are. The comparison would look something like this:
Assumptions associated with finding the physics: The springs are the same length, the springs have the same k values chosen to be at 500 N/m, the connection points of the springs have negligible masses, and there are no outside forces aside from the one applied force. The goal now is to find the strength of the initial force if Spring 2 were stretched 4 centimeters or 0.04 meters. This is quite simple using Hooke’s Law:
F = -kx
F= -(500 N/m)(0.04 m)
F= 20 N
Now the force applied to Spring 1 if it were stretched 2 centimeters or 0.02 meters, after Spring 2 was stretched, and can be calculated using the given k constant, F, and Hooke’s Law:
F= -(500 N/m)(0.02 m)
F= 10 N
While the force has decreased, it is still existent and if there were many more identical springs attached to these two, with the same k constants, the applied force could be calculated for the other springs as well. Theoretically, there could be an infinite number of springs under these conditions, but they would eventually feel a force, no matter how small.
This goes to show that there could be hundreds or thousands of metronomes, and they would still communicate and eventually synchronize.