Your 'pearl pendulum' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Your general comment, if any: **
** Your description of the rhythm of the pendulum when tilted 'back' **
The sounds start out pretty fast and get closer together as they get quieter and finally fade out.
** Your description of the rhythm of the pendulum when tilted 'forward' **
The sounds are definitely slower than the previous one. They are more even but do slow down a bit as they fade out.
** Your description of the process used to keep the rhythm steady and the results you observed: **
I slid part of a pad of paper under one end of the bracket. I then slid the bracket back and forth until I could see the space between ball and bracket. I then backed it up a bit until they just touched.
The sounds steady, but harder to tell as it went along because they got quieter.
** Your description of what happened on the tilted surface (textbook and domino), rotating the system 45 degrees at a time: **
bracket w/ pend facing downhill: sounds got a little bit slower.
1/4 turn clockwise: gets slightly faster, doesn't last long
1/4 turn clockwise: sounds get faster
1/4 turn clockwise: sounds are slightly faster than original, but doesn't last long
** Your description of how you oriented the bracket on the tilted surface to obtain a steady rhythm: **
bracket oriented with pendulum facing downhill obtains most regular beat.
** Your report of 8 time intervals between release and the second 'hit': **
.453
.516
.5
.484
.484
.469
.453
.437
Time between release of pendulum and when it hits the bracket the second time. From start in, back out, and back in.
** Your report of 4 trials timing alternate hits starting with the second 'hit': **
.406, .688, .609, .844
.5, .531, .672, .719
.393, .563, .641, .656
.453, .734, .813, .719
The time intervals between start and second hit, second hit and fourth hit, fourth hit and sixth hit, sixth hit and eighth hit. I used the timer program and clicked the mouse button for each timed hit.
** The length of your pendulum in cm (you might have reported length in mm; the request in your instructions might have been ambiguous): **
Pendulum is 9.3cm
** Your time intervals for alternate 'hits', starting from release until the pendulum stops swinging: **
.438, .629, .684, .735
** Your description of the pendulum's motion from release to the 2d hit: **
The pendulum moves from extreme point to the strike point
** Your description of the pendulum's motion from the 2d hit to 4th hit: **
Pendulum moves from strike point almost back to original extreme point and back to strike point.
The first hit is only half of a cycle and the first hit to second hit is a complete cycle.
** Your description of the difference in the pendulum's motion from release to the 2d 'hit', compared to the motion from the 2d 'hit' to the 4th hit: **
The motion from release to second hit is 1 1/2 cycles and the motion from second hit to fourth hit is two complete cycles.
A cycle goes from extreme pt to equilibrium to opposite extreme pt to equilibrium then back to the original point. The bracket interrupts the cycle at its middle, but from 'hit' to extreme to 'hit' is one half-cycle. That is, from one 'hit' to the next is 1/2 cycle.
Modifying your response accordingly, you get respective results of 3/4 cycle and 1 cycle.
** Your description of the difference in the pendulum's motion from the 2d to the 4th 'hit' compared to the motion from the 4th to 6th hit: **
They are the same number of cycles, however with each strike the pendulum transfers energy and therefore loses energy. The cycle becomes smaller. With each cycle the pendulum doesn't quite make it to the last extreme point.
** Your conjecture as to why a clear difference occurs in some intervals vs. others: **
The first time interval should be shorter because it is only 1 1/2 cycle rather than 2 full cycles
** What evidence is there that subsequent intervals increase, decrease or remain the same: **
Subsequent time intervals should slow down because the pendulum is losing energy with each cycle.
The pendulum was set up so that the time between 'hits' doesn't change. The 'pearl' travels less distance with each subsequent half-cycle, but that distance is traveled at a lesser average speed, so the time between 'hits' remains constant.
** What evidence is there that the time between 'hits' is independent of the amplitude of the swing? **
By placing the strike plate (bracket) in the way of the pendulum's swing (causing the pendulum to not be able to go through it's entire extreme to other extreme cycle it shortens how far it actually swings. Therefore the length of the swing was dependent on how far it could actually swing, and not dependent solely on how long the string was.
I believe the question was related to the time between 'hits' for a given setup. The amplitude of the swing (distance from equilibrium point to extreme position) clearly decreased with each 'hit'. To the extent that the rhythm of the pendulum was constant, the time between 'hits' therefore appears to be independent of the amplitude of the swing.
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Just over 1 hour to complete, 45 mins to type up and figure out the last question
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I have NO confidence in my ability to time the intervals accurately
Very good work.
There was some variation in your times. Your results are neverthless consistent with expected ratios. What this tells us is that the pendulum is a more accurate timing device than a human-triggered timer.