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' **
At first, the rhythm of the sounds are steady, and then as the pearl begins to stop bouncing, the rhythms become faster and closer together. I heard the click noises of the bounces become closer together and more quiet as the pearl started to come to a stop.
** Your description of the rhythm of the pendulum when tilted 'forward' **
The rhythm of the sounds get further apart as the pearl begins to stop bouncing. It also becomes slower and more quiet as the pearl begins to stop. At first, the pearl bounced faster and the sound was louder, then it became to become slower and more soft.
** Your description of the process used to keep the rhythm steady and the results you observed: **
I placed the bracket on a text book that was lying on a table. I used a thin piece of folded paper as a shim on the front end to adjust the level of the bracket. I pulled the pearl back and released it, making it bounce against the bracket. The pearl bounced very steadily against the bracket until it stopped bouncing. The pearl bounced about 28 times before it came to a complete stop.
** Your description of what happened on the tilted surface (textbook and domino), rotating the system 45 degrees at a time: **
The orientation of the bracket was in the middle of the book with the base of the bracket parallel to one of the sides of the book and the face of the bracket facing toward the end where the dominoes were placed under the book. The sounds seemed to get closer together when the pendulum was released.
The orientation of the bracket was then rotated 45 degrees counterclockwise toward the corner of the book where the domino was under. The sounds still seemed to get closer together as the pendulum kept swinging.
The orientation of the bracket is now facing the side of the book where it would be opened at, 90 degrees. The sounds of the pendulum seemed to be steady at first, but then seem to be closer together and then slow down and became more quiet as it began to come to a stop.
The bracket is now positioned at 135 degrees on the text book. It is facing the corner beside the 45 degree angle. The pendulum seems to still be steady, probably even more steady then the 90 degrees. The sounds are very steady and do not seem to slow down or get faster.
The pendulum is now positioned at 180 degrees on the text book, facing the opposite direction of the dominoes where the first position was. The sounds of the pendulum seem to be further apart than the other times and also seemed to be slower.
The pendulum is now positioned at 225 degrees, facing the across from the 45 degree angle. The rhythm of the sounds of the pendulum seemed to be far apart and slower, even more so than the 180 degree position. The sounds seemed to be more quiet as the pendulum came to a stop.
The position is now at 270 degrees, facing the side of the book that is bound together. The sounds of the pendulum seem to be pretty steady and do not seem to speed up or slow down. The rhythm seems to be steady, even as the pendulum began to come to a stop.
The bracket is placed at a 315 degree angle, facing the top corner, atop of the domino. The rhythm of the sounds of the pendulum seem to be closer together and they speed up as the pearl is coming to a stop. The sound also seems to become more quiet as the sound become closer together.
The position is now back at its original position, 360 degrees. It is in the middle of the book, facing the top of the book where the dominoes have propped it up. The rhythm of the sounds of the pendulum seem to get closer together and slower as it is released.
** Your description of how you oriented the bracket on the tilted surface to obtain a steady rhythm: **
I would position the bracket at the 270 degree angle, in the middle of the text book, facing the bound side of the book because this is the position where the bracket seemed to be the most steady.
** Your report of 8 time intervals between release and the second 'hit': **
.391
.422
.391
.422
.453
.453
.438
.438
These numbers represent the time interval of time between when the pendulum was released and when it hit the bracket for the second time. I obtained these numbers by using the TIMER program and clicking on the button at the same time i released the pendulum and the same time the pendulum hit the bracket on the second time.
** Your report of 4 trials timing alternate hits starting with the second 'hit': **
.438, .500, .531, .516
.468, .501, .531, .523
.453, .469, .563, .547
.453, .516, .578, .565
These results are the time intervals in which the pendulum was first released and for each 2 hits made on the bracket from the pearl. These results were obtained by using the TIMER program. I clicked the button as soon as the pendulum was released and then clicked again every other time the pendulum hit the bracket.
** The length of your pendulum in cm (you might have reported length in mm; the request in your instructions might have been ambiguous): **
9.3 centimeters
** Your time intervals for alternate 'hits', starting from release until the pendulum stops swinging: **
.044, .054, .013
** Your description of the pendulum's motion from release to the 2d hit: **
The motion of the pendulum between release and the first 'hit' was released from an 'extreme point' and then stroke the bracket at its equilibrium point, then came below, close to its original 'extreme point'.
** Your description of the pendulum's motion from the 2d hit to 4th hit: **
The motion of the first hit and the second hit started at the pendulum's equilibrium point from where it hit, then went below its 'extreme point' then back to the equilibrium point for the second hit. This motion differs from the previous motion because it is starting at its equilibrium point, not the extreme point.
** 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 between release and the second hit differs from the motion between the second hit and the fourth hit. The motion from release started at the extreme point and then came halfway back to the extreme point after the second hit. The motion from the second hit started at the area where it hit, the equilibrium, and then came back to the equilibrium point for the fourth hit.
&#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 &#
&#Please respond with a copy of this question, a copy of any other part of this document you wish to include, and your response to the question. Indicate your response using the symbols *&##. As your title use the 'response title' suggested above (just copy and paste that title into the Title box of the Submit Work form); if no suggested title was given use your own title.
&#
** 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: **
These motions differ because motion from the second to the fourth hit is further apart than the motion from the fourth hit to the sixth. The fourth hit and the sixth hit become closer together because it is coming closer to stopping. It is also faster than the second hit and the fourth.
** Your conjecture as to why a clear difference occurs in some intervals vs. others: **
Because they pendulum is being released from its extreme point at release, causing the pendulum to strike the bracket at a faster pace because of more force.
** What evidence is there that subsequent intervals increase, decrease or remain the same: **
You would expect them to decrease because the hits become shorter together because the pendulum is not being released all the way from its extreme point each time.
** What evidence is there that the time between 'hits' is independent of the amplitude of the swing? **
It is against because the length of the pendulum's swing becomes shorter the more times it swings because it is preparing to come to its equilibrium point.
** **
about 1 hour
** **
Good work, but your description of the differences in the two motions and your expected ratio need more detail. Please respond as requested above.
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' **
At first, the rhythm of the sounds are steady, and then as the pearl begins to stop bouncing, the rhythms become faster and closer together. I heard the click noises of the bounces become closer together and more quiet as the pearl started to come to a stop.
** Your description of the rhythm of the pendulum when tilted 'forward' **
The rhythm of the sounds get further apart as the pearl begins to stop bouncing. It also becomes slower and more quiet as the pearl begins to stop. At first, the pearl bounced faster and the sound was louder, then it became to become slower and more soft.
** Your description of the process used to keep the rhythm steady and the results you observed: **
I placed the bracket on a text book that was lying on a table. I used a thin piece of folded paper as a shim on the front end to adjust the level of the bracket. I pulled the pearl back and released it, making it bounce against the bracket. The pearl bounced very steadily against the bracket until it stopped bouncing. The pearl bounced about 28 times before it came to a complete stop.
** Your description of what happened on the tilted surface (textbook and domino), rotating the system 45 degrees at a time: **
The orientation of the bracket was in the middle of the book with the base of the bracket parallel to one of the sides of the book and the face of the bracket facing toward the end where the dominoes were placed under the book. The sounds seemed to get closer together when the pendulum was released.
The orientation of the bracket was then rotated 45 degrees counterclockwise toward the corner of the book where the domino was under. The sounds still seemed to get closer together as the pendulum kept swinging.
The orientation of the bracket is now facing the side of the book where it would be opened at, 90 degrees. The sounds of the pendulum seemed to be steady at first, but then seem to be closer together and then slow down and became more quiet as it began to come to a stop.
The bracket is now positioned at 135 degrees on the text book. It is facing the corner beside the 45 degree angle. The pendulum seems to still be steady, probably even more steady then the 90 degrees. The sounds are very steady and do not seem to slow down or get faster.
The pendulum is now positioned at 180 degrees on the text book, facing the opposite direction of the dominoes where the first position was. The sounds of the pendulum seem to be further apart than the other times and also seemed to be slower.
The pendulum is now positioned at 225 degrees, facing the across from the 45 degree angle. The rhythm of the sounds of the pendulum seemed to be far apart and slower, even more so than the 180 degree position. The sounds seemed to be more quiet as the pendulum came to a stop.
The position is now at 270 degrees, facing the side of the book that is bound together. The sounds of the pendulum seem to be pretty steady and do not seem to speed up or slow down. The rhythm seems to be steady, even as the pendulum began to come to a stop.
The bracket is placed at a 315 degree angle, facing the top corner, atop of the domino. The rhythm of the sounds of the pendulum seem to be closer together and they speed up as the pearl is coming to a stop. The sound also seems to become more quiet as the sound become closer together.
The position is now back at its original position, 360 degrees. It is in the middle of the book, facing the top of the book where the dominoes have propped it up. The rhythm of the sounds of the pendulum seem to get closer together and slower as it is released.
** Your description of how you oriented the bracket on the tilted surface to obtain a steady rhythm: **
I would position the bracket at the 270 degree angle, in the middle of the text book, facing the bound side of the book because this is the position where the bracket seemed to be the most steady.
** Your report of 8 time intervals between release and the second 'hit': **
.391
.422
.391
.422
.453
.453
.438
.438
These numbers represent the time interval of time between when the pendulum was released and when it hit the bracket for the second time. I obtained these numbers by using the TIMER program and clicking on the button at the same time i released the pendulum and the same time the pendulum hit the bracket on the second time.
** Your report of 4 trials timing alternate hits starting with the second 'hit': **
.438, .500, .531, .516
.468, .501, .531, .523
.453, .469, .563, .547
.453, .516, .578, .565
These results are the time intervals in which the pendulum was first released and for each 2 hits made on the bracket from the pearl. These results were obtained by using the TIMER program. I clicked the button as soon as the pendulum was released and then clicked again every other time the pendulum hit the bracket.
** The length of your pendulum in cm (you might have reported length in mm; the request in your instructions might have been ambiguous): **
9.3 centimeters
** Your time intervals for alternate 'hits', starting from release until the pendulum stops swinging: **
.044, .054, .013
** Your description of the pendulum's motion from release to the 2d hit: **
The motion of the pendulum between release and the first 'hit' was released from an 'extreme point' and then stroke the bracket at its equilibrium point, then came below, close to its original 'extreme point'.
** Your description of the pendulum's motion from the 2d hit to 4th hit: **
The motion of the first hit and the second hit started at the pendulum's equilibrium point from where it hit, then went below its 'extreme point' then back to the equilibrium point for the second hit. This motion differs from the previous motion because it is starting at its equilibrium point, not the extreme point.
** 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 between release and the second hit differs from the motion between the second hit and the fourth hit. The motion from release started at the extreme point and then came halfway back to the extreme point after the second hit. The motion from the second hit started at the area where it hit, the equilibrium, and then came back to the equilibrium point for the fourth hit.
&#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 &#
&#Please respond with a copy of this question, a copy of any other part of this document you wish to include, and your response to the question. Indicate your response using the symbols *&##. As your title use the 'response title' suggested above (just copy and paste that title into the Title box of the Submit Work form); if no suggested title was given use your own title.
&#
** 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: **
These motions differ because motion from the second to the fourth hit is further apart than the motion from the fourth hit to the sixth. The fourth hit and the sixth hit become closer together because it is coming closer to stopping. It is also faster than the second hit and the fourth.
** Your conjecture as to why a clear difference occurs in some intervals vs. others: **
Because they pendulum is being released from its extreme point at release, causing the pendulum to strike the bracket at a faster pace because of more force.
** What evidence is there that subsequent intervals increase, decrease or remain the same: **
You would expect them to decrease because the hits become shorter together because the pendulum is not being released all the way from its extreme point each time.
** What evidence is there that the time between 'hits' is independent of the amplitude of the swing? **
It is against because the length of the pendulum's swing becomes shorter the more times it swings because it is preparing to come to its equilibrium point.
** **
about 1 hour
** **
Good work, but your description of the differences in the two motions and your expected ratio need more detail. Please respond as requested above.