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 get closer together as the bracket is leadned back. (ie. the rhythm gets faster)
** Your description of the rhythm of the pendulum when tilted 'forward' **
The sounds get further apart, meaning that the rhythm of the ball bouncing off the bracket gets slower as the bracket is tilted forwards.
** Your description of the process used to keep the rhythm steady and the results you observed: **
I placed the bracket on a kitchen counter, then placing a penny under the far corner in order to make it completely level, as so the pearl was just bairly touching the bracket. When i pulled it back, the pearl hit the bracket approx. 6 or 7 times (The end bounces are sometime hard to count when they become so close together).
** Your description of what happened on the tilted surface (textbook and domino), rotating the system 45 degrees at a time: **
When placed on the book, which was slightly tilted by putting a domino under both the top right and top left corner, the bracket was tilted back just a little bit, causing the pearl to speed up its rhythm.
When rotating it the first 45 degrees, i noticed that the pearl was not hitting in the center of the bracket anymore, but off to the side a little bit.
When rotating to the 90 degree position, the pearl was barly hitting the edge of the bracket at all, but the beats seemed to be constant.
Another 45 degrees: The rhythm seems to be decreasing and becoming slower
180 degrees: The rhythm is slowest
Another 45 degrees: The rhythm begins speeding up once again, but very slowly.
270 degrees: The rhythm is once again at a constant speed.
Another 45 degrees: Speeding up still
360 degrees: The rhythm is at its fastest
** Your description of how you oriented the bracket on the tilted surface to obtain a steady rhythm: **
Either at the 90 degree rotation or the 270 degree rotation.
** Your report of 8 time intervals between release and the second 'hit': **
1.0
1.03
0.81
1.09
0.97
1.09
0.80
0.98
** Your report of 4 trials timing alternate hits starting with the second 'hit': **
1.063, 1.016, .828, .672
1.172, .922, .813, .656
1.0, .859, .688, .563
.938, .797, .641, .531
These results are the times for when the pearl his the bracket on the 2nd bounce, the 4th bounce, the 6th bounce, and the 8th bounce. I found these numbers by simply clicking the time for this number of bounce.
** The length of your pendulum in cm (you might have reported length in mm; the request in your instructions might have been ambiguous): **
18 cm
** Your time intervals for alternate 'hits', starting from release until the pendulum stops swinging: **
.047, .188, .156
.25, .109, .157
.141, .171, .125
.141, .156, .11
** Your description of the pendulum's motion from release to the 2d hit: **
When release it is being released from its origional extreme point. When it hits the bracket the first time, it is not expecting to be stopped, so it hits with an extreme force and bounces of back in the direction of its origional extream point.
** Your description of the pendulum's motion from the 2d hit to 4th hit: **
After the first hit, the pearl bounces off in the same direction it came from, with less speed and force. once reaching its maximum height it again heads in the direction of the bracket, only to bounce off it again for a second time. This motion differes from the first motion of release because it has less force and velocity, with its peak position lower than the first.
** 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: **
Again, the pearl is losing power and speed, causing the hits to become closer together in 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: **
Same as before, the pearl is still losing power and momentum, thus causing it to hit the bracket at a faster rate.
&#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 conjecture as to why a clear difference occurs in some intervals vs. others: **
Because the pearl is moving at a faster speed.
** What evidence is there that subsequent intervals increase, decrease or remain the same: **
stay roughtly the same
** What evidence is there that the time between 'hits' is independent of the amplitude of the swing? **
because the pearl is only going half the distance of a true pendulum swing, yet still acts in the pendulum motion, instead of just coming to a complete stop after hitting the bracket the first time.
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20 min
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Overall good, butplease respond as requested in my note.