More about Pendulums... 2/27

Last Monday we continued working on our circuit with the motor and the pendulum. But before we did anything our professor lectured us about “circuit hygiene.” Until Monday I had been building my circuits without paying attention to which colors of wires I was using or how long I cut my wires. I often added extra wires that weren’t necessary instead of just attaching one component directly to another component. Our professor stressed the importance of circuit hygiene. He said that many times the reason that our circuits did not work was because our wires were simply too long. Long wires add extra resistance to the circuit. They also make the circuit hard to understand and debug. Also, hygienic circuits are just more aesthetically appealing! I think that it is important that as we learn to build circuits we avoid picking up bad habits.
    After we all spent some time cleaning up our circuits we went back to playing with our pendulums.  Our circuit had two potentiometers on it: one in parallel with the motor and one connected to ground in the integrator. The potentiometer parallel to the motor controlled the speed that the pendulum swung. The potentiometer in the integrator controlled the frequency of the pendulum, since:
                                                               V= V+ + (1/RC) ∫ V+ dt
I think that changing the resistance is kind of like changing the k constant in a mechanical spring where:
                                                                          F=kx.
  If we did not have both of our potentiometers set right our system would have either too much positive feed back or too much negative feedback. Our professor used the analogy of a ball attached to two springs to describe the situation. For example, if the system had too much positive feedback it was unstable because it was like a ball on top of a steep mountain, and it would roll of the top no matter what the springs where doing. If the system had too much negative feedback it wouldn’t do anything because it was like a ball in a valley that would not roll either way because of gravity.  We had to adjust our potentiometers so that the circuit was like a ball attached to two springs on a level surface, where the only force acting on the ball would be the springs themselves.
    With our oscilloscopes we were able to plot the speed of speed of the pendulum verses its position. Typically a speed vs. position graph of a pendulum would look like this:

But this graph depicts a pendulum that slows down. Since we could control the speed of our pendulum our graph just made a misshapen circle. When the frequency was really high it made more of a parallelogram.