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 rhythm gets faster.
** Your description of the rhythm of the pendulum when tilted 'forward' **
The sounds get closer together. The pearl made one bounce and then many bounces afterward very close together.
** Your description of the process used to keep the rhythm steady and the results you observed: **
I tilted the bracket backward slightly so that when stationary the pearl is about one inch away from the bracket. That then made the pearl bounce in a steady rhythm.
** Your description of what happened on the tilted surface (textbook and domino), rotating the system 45 degrees at a time: **
First I placed two dominos one side of a textbook at each corner. Then I placed the bracket in the center of the textbook without changing its angle at all. I pulled the pearl back and released and it made a somewhat steady rhythm. Then I rotated the braket 45 degrees and the rhythm became a little faster. As you rotate 45 degrees for each progression of tests you find that it speeds up until it reaches 180 degrees and then it starts to slow down again.
** Your description of how you oriented the bracket on the tilted surface to obtain a steady rhythm: **
I oriented the braket to where it is leaning back slightly. Somewhere around 85 degrees.
** Your report of 8 time intervals between release and the second 'hit': **
.758
.770
.765
.734
.798
.777
.750
.761
These numbers tell us how long it took for the pearl to be released take one bounce and then hit the braket once again.
** Your report of 4 trials timing alternate hits starting with the second 'hit': **
.760, .777, .789
.758, .771, .798
.770, .789, .794
.756, .762, .761
These results are time between bounces and this tells us how friction slows motion.
** The length of your pendulum in cm (you might have reported length in mm; the request in your instructions might have been ambiguous): **
58.42cm
** Your time intervals for alternate 'hits', starting from release until the pendulum stops swinging: **
.761, .774, .785
** Your description of the pendulum's motion from release to the 2d hit: **
To rephrase the pearl makes a full cycle when it travels from release point to extreme back to release point (almost) and them back to the extreme point.
note that the pearl starts at an extreme point when you release it, but is not at an extreme point when it makes the second 'hit'
** Your description of the pendulum's motion from the 2d hit to 4th hit: **
The first hit is fairly fast but then the pearl does not reach back as far so it hits a little faster. Then the next hit is even quicker.
** 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: **
Motion of the first hit is heavy and fast while the hit of the second is a little faster just because the pearl does not reach back as far.
&#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 &#
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** 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: **
It gets quicker and quicker with more and more hits because the pearl does not have to travel as far.
** Your conjecture as to why a clear difference occurs in some intervals vs. others: **
Because it has more force behind the pearl.
** What evidence is there that subsequent intervals increase, decrease or remain the same: **
Probably increase because the pearl does not have to travel as far between hits.
** What evidence is there that the time between 'hits' is independent of the amplitude of the swing? **
This experiment provides evidence against the hypothesis because after conducting it we find no significant difference.
** **
45 minutes
** **
Your times are consistent with a pendulum of the reported length, so it looks like you have good data, except for release to 2d 'hit', which should differ from the times recorded for subsequent alternate 'hits'.
See my note and please respond as indicated.