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 sound of the pendulum is getting faster so the rhythm is getting faster.
** Your description of the rhythm of the pendulum when tilted 'forward' **
The rhythm gets slower so the sound of the pendulum hitting the bracket gets slower.
** Your description of the process used to keep the rhythm steady and the results you observed: **
I put the bracket on a piece of level styrofoam and the pendulum hit the bracket steadily at 11 times.
** Your description of what happened on the tilted surface (textbook and domino), rotating the system 45 degrees at a time: **
At 0 degrees the rhythm is constant.
At 45 degrees the rhythm is faster and gets slower.
At 90 degrees the rhythm is faster and gets slower.
At 135 degrees the rhythm is faster and gets slower.
At 180 degrees the rhythm is constant.
At 225 degrees the rhythm is slow then speeds up.
At 270 degrees the rhythm is slow then speeds up.
At 315 degrees the rhythm is slow then speeds up.
At 360 degrees the rhythm is constant.
** Your description of how you oriented the bracket on the tilted surface to obtain a steady rhythm: **
At 0 degree, 180 degree and 360 degree angles the pendulum has the most regular beat.
** Your report of 8 time intervals between release and the second 'hit': **
.484
.688
.531
.578
.468
.453
.500
.437
** Your report of 4 trials timing alternate hits starting with the second 'hit': **
0.453, 0.515, 0.531, 0.547
0.406, 0.594, 0.671, 0.748
0.516, 0.641, 0.609, 0.641
0.500, 0.531, 0.563, 0.595
** The length of your pendulum in cm (you might have reported length in mm; the request in your instructions might have been ambiguous): **
8.500 cm
** Your time intervals for alternate 'hits', starting from release until the pendulum stops swinging: **
0.52, 0.04, 0.03
** Your description of the pendulum's motion from release to the 2d hit: **
After the pendulum is released in moves down in vertical measurement and hits the bracket then moves back up in vertical measurement.
** Your description of the pendulum's motion from the 2d hit to 4th hit: **
This motion does not return the pendulum all the way back to the initial starting position.
** 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: **
This motion has a longer time because the pendulum goes a longer distance then it does when it hits for the second and fourth time.
** 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 closely constant in speed and time.
&#A full cycle of a free pendulum is from extreme point to equilibrium to opposite extreme point then back to equilibrium and finally back to (almost) the original extreme point. The pearl pendulum is released from an 'extreme point' and strikes the bracket at its equilibrium point, so it doesn't get to the opposite extreme point.Thus the period of the pendulum can be divided into four parts. From the steadiness of the rhythm we have good evidence that the motion between 'hits' takes the same time independent of the amplitude of the motion (the rhythm remains constant while the amplitude of the motion decreases). Theoretically each of the four parts of the cycle, as described above, takes the same time. Assuming this to be true, we can speak of the quarter-cycle from an extreme point to equilibrium or from equilibrium to an extreme point.
Through how many quarter-cycles does the pendulum move between release and the second 'hit'?
Through how many quarter-cycles does it move between the second and the fourth 'hit'?
What therefore should be the ratio of the time interval from 2d to 4th 'hit', to the interval from release to the 2d 'hit'?
How does this ratio compare with the results you just reported?
Does this constitute evidence for or against the theoretical hypothesis that the quarter-cycles all require the same time?Suggested response title: description of motion of pearl pendulum &#
** Your conjecture as to why a clear difference occurs in some intervals vs. others: **
The pendulum will be moving at its fastest rated during the first time interval after 1 hit and between the second hit.
** What evidence is there that subsequent intervals increase, decrease or remain the same: **
They should stay the same based on previous data from the beginning of the experiment.
** What evidence is there that the time between 'hits' is independent of the amplitude of the swing? **
The longer the pendulum the longer the actual swing, which is more time in between each hit.
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It took an hour and a half because I had to start over.
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Good work. Please respond as requested to the question posed in my notes so we can more specifically interpret these results.