I've recently done an experiment where I analyzed a mass moving in circular motion around a point with a spring attached to the mass on one end and to the point around which the mass moves on the pother end. This system was set on top of an air table to reduce friction as much as possible and it was recorded using a camara set on top of the table.
After analyzing the video using the program Tracker. Then, using Kaleidagraph I got the polar coordinates as well as the time derivatives of the radius and the angle. With this data, I got the hamiltonian of the system and it doesn't remain constant.
According to the theory, as the holonomic constraints are stationary in this system then the hamiltonian should be exactly equal to the mechanical energy which should remain constant. Instead, what I get is some oscilating value which decreases.
The fact that it oscilates downwards makes sense as this could be attributed to a friction force we are neglecting. However, it doesn't make sense that the energy of the system oscilates. In fact, this oscilation correlates with the oscilation of the radius (the distance between the point the mass orbits and the mass). This correlation makes me think that there could be some reason for why the energy doesn't remain constant but I still can't explain why this happens.
One think I've thought of while representing some of the variables is that the velocity of the system could have something to do with the change in the hamiltonian not from a physics point of view but more on a technical way. As when the velocity is larger the camara couldn't capture the image properly and thus could create some error.
Other than this last interpretation I have no idea why the energy would change and why this change would be correlated to the change in r.
If anyone had some insights on why this happens I would appreciate the help.
Sorry for any bad grammar or spelling, english is not my first language.