Your 'cq_1_10.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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A pendulum requires 2 seconds to complete a cycle, which consists of a complete back-and-forth oscillation (extreme point to equilibrium to opposite extreme point back to equilibrium and finally to the original extreme point). As long as the amplitude of the motion (the amplitude is the distance from the equilibrium position to the extreme point) is small compared to the length of the pendulum, the time required for a cycle is independent of the amplitude.
• How long does it take to get from one extreme point to the other, how long from an extreme point to equilibrium, and how long to go from extreme point to equilibrium to opposite extreme point and back to equilibrium?
If a pendulum takes 2 seconds to complete an oscillation, it would take 1 second to get from one extreme point to the other, ½ a second to get to equilibrium, and 1 and 1/2 seconds to go from extreme point to equilibrium to opposite extreme point and back to equilibrium.
answer/question/discussion:
• What reasonable assumption did you make to arrive at your answers?
I assumed that the pendulum traveled with practically a constant velocity except when it would change direction. The maximum velocity occurs when the pendulum is cenetered, or at equilibrium, but it would take the same time to go from one side to another.
answer/question/discussion:
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10 minutes
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You need only assume that the times from equilibrium to extreme point and from extreme point to equilibrium are equal, and that these times do not vary with the pendulum's decreasing amplitude. There is no reason to assume that this constancy of rhythm is in any way related to constant velocity or to conservation of the pendulum's energy; it is in fact obvious that neither of these conditions holds.
At this stage of the course we aren't in a position to explain the constant rhythm; we simply observe that if we set up the pendulum correctly this appears, within our limits of experimental error, to be the case.
The actual explanation is pretty deep. In fact, we can't explain this phenomenon within the mathematical constraints of this course. The explanation involves a lot of calculus and differential equations, at a pretty advanced level. We do the calculus of the ideal case (no energy loss) later in the University Physics course, but it takes more than a year of the calculus prerequisite to consider damping and other factors involved in non-ideal cases, so these cases are beyond the scope of this course. It does turn out that when the calculus is refined for a non-ideal pendulum like this one, a pendulum that does lose energy, we find that there are indeed tiny variations in the period and between the quarter-cycles. This is not something we can observe without sophisticated and highly accurate electronic timers, so the variations aren't relevant to this course, but they do exist.