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' **
Rhythm gets faster with bracket tilted backwards so the pearl rests on the bracket.
I closed my eyes and listened to the sounds and felt that the rhythm got faster
** Your description of the rhythm of the pendulum when tilted 'forward' **
The rhythm slows down when the bracket is tilted forward.
Again, I closed my eyes and listened carefully several times.
** Your description of the process used to keep the rhythm steady and the results you observed: **
I put a postcard under the front of the bracket until the ball barely touched the bracket. The rhythm was very steady and the pendulum hit the bracket 16 times.
** Your description of what happened on the tilted surface (textbook and domino), rotating the system 45 degrees at a time: **
Original position is the bracket aligned with the book from top to bottom with the pearl facing down. In this position the sounds got further apart. Next turned the bracket 45 degrees so that the pearl was facing SE on a compass. In this position the sounds still got further apart. Then turned so that the pearl was facing East on a compass and the sounds still got further apart. Turned it 45 degrees so the pearl was facing NE and the rhythm remained constant. Turned the pearl facing due North (top of the book) and the rhythm increased. Turned it 45 degrees facing NW and the sounds remained steady. Turned 45 degrees facing West and the sound remained steady. Turned 45 degrees facing SW and the rhythm slowed.
** Your description of how you oriented the bracket on the tilted surface to obtain a steady rhythm: **
I would orient the bracket either West or NE to obtain the most regular rhythm.
** Your report of 8 time intervals between release and the second 'hit': **
.333
.337
.329
.330
.340
.325
.355
.318
This is the time intervals between 8 hits of the pearl. The pearl bounced a total of 14 times I did not time the first hit and stopped at hit number 9.
** Your report of 4 trials timing alternate hits starting with the second 'hit': **
.670, .650, .680, .630
.623, .652, .684, .670
.668, .700, .592, .656
.620, .550, .690, .700
Timed every other hit of the pendulum and the rhythm was very regular but there is error in my timing.
** The length of your pendulum in cm (you might have reported length in mm; the request in your instructions might have been ambiguous): **
93 mm
** Your time intervals for alternate 'hits', starting from release until the pendulum stops swinging: **
I had so much spread in my data that the answer to this question would be different for each trial. Not sure.
** Your description of the pendulum's motion from release to the 2d hit: **
The pearl is released from an extreme and travels back to equilibrium but does not get to the opposite extreme point.
** Your description of the pendulum's motion from the 2d hit to 4th hit: **
The pearl bounces off the bracket and returns toward the original extreme position but only part way.
** 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 distance traveled by the pearl and its velocity reduce with every hit.
** 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: **
Again, velocity and displacement of the pearl continues to drop.
** Your conjecture as to why a clear difference occurs in some intervals vs. others: **
I wouldn't expect it to be shorter and my data showed that it changed very little.
** What evidence is there that subsequent intervals increase, decrease or remain the same: **
Based on my experience with this experiment if the equilibrium position of the pearl is precisely even with the face of the bracket I would expect the intervals to remain constant.
** What evidence is there that the time between 'hits' is independent of the amplitude of the swing? **
I'm not sure I understand the second part of the question, but shortening the string definitely reduces the length of the swing and speeds the rhythm of the hits.
The amplitude of the swing is the distance between the equilibrium and extreme points of the motion.
If the rhythm remains constant then, since the amplitude progressively decreases, there is good evidence that the time between 'hits' is independent of the amplitude. This wouldn't be the case if the amplitude was too great--if you pull the pendulum back more than about 30 deg from vertical you start to get an observable decrease in the period of oscillation. One within the 30 degree range the period stays very nearly steady, and the deviations from steady rhythm approach zero very quickly with further decreases in amplitude.
You know calculus so when we study simple harmonic motion we can actually address this question, if at that time you are so inclined.
Assuming constant rhythm due to a constant time interval between equlibrium and extreme points, what should be the ratio of the time intervals between release and the first 'hit', to time intervals between alternate subsequent 'hits'. You previously described, correctly, the differences in the motion of the pendulum.
How well do your data match these predictions?
&#Can you send me a note with a copy of this question, your answers, my notes and your modified answers (and/or questions) indicated by &&&&? &#
** **
1.5 hours
** **
Good work. Please respond to my one question, as indicated above.