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 starts steady for the first few clicks, then the sounds get closer together.
This is consistent with the usual observation.
** Your description of the rhythm of the pendulum when tilted 'forward' **
The sounds start out further apart for about 3 clicks, then they suddenly get very close together, or faster.
If the system is tilted forward, so that the stationary 'pearl' hangs significantly away from the bracket, we consistently observe that the sounds get further apart.
** Your description of the process used to keep the rhythm steady and the results you observed: **
In order to produce a steady rhythm on an even surface, I had to shim the front of the bracket, so the bracket was tilted back slightly, I just had to use a subscription card from a magazine. It was steady for about 8 clicks, but then became a series of faster clicks before stopping.
** Your description of what happened on the tilted surface (textbook and domino), rotating the system 45 degrees at a time: **
Position of bracket is the hour-hand of a clock during the times listed (or 45 degree intervals).
12:00- Closer
10:30- Closer
9:00- Further
7:30- Further
6:00- Further
4:30- Further
3:00- Further
1:30- Closer
** Your description of how you oriented the bracket on the tilted surface to obtain a steady rhythm: **
The most regular beat seemed to be at 6:00.
** Your report of 8 time intervals between release and the second 'hit': **
.578
.656
.500
.469
.547
.500
.510
.531
These are the intervals in seconds between the release of the pearl and its second strike on the bracket. Obtained by simultaneously releasing pearl and initiating timer, then clicking timer upon second strike.
** Your report of 4 trials timing alternate hits starting with the second 'hit': **
.496, .609, .641, .689, .750, .766, .906, .938, 1.049
.516, .625, .688, .688, .719, .797, .859, .984
.516, .672, .688, .703, .750, .781, .938, .969
.469, .641, .688, .719, .734, .766, .934, .953
These results are time in seconds of every other pedulum strike on the bracket, and you can see that as with each set of clicks, the pendulum is slowing down. They were obtained by simultaneously releasing pearl and initiating timer, then clicking the timer upon every other strike of the bracket until the pearl stopped making audible contact with the bracket.
If some orientations result in increasingly frequent strikes, and some in decreasing frequency, then there should be an orientation where the strikes remain very nearly constant in frequency. The 6:00 position appears to be right in the middle of the 'further' range; unless the table is warped this is the position where the maximum increase in time between strikes would be expected. The most regular strikes would be expected between your reported 10:30 and 9:00 positions, and between 3:00 and 1:30.
** The length of your pendulum in cm (you might have reported length in mm; the request in your instructions might have been ambiguous): **
93mm
** Your time intervals for alternate 'hits', starting from release until the pendulum stops swinging: **
.493, .637, .676secs
** Your description of the pendulum's motion from release to the 2d hit: **
The motion between the release and first hit is sort of like a tethered free fall, with sort of an arc like motion into the bracket. Upon release it strikes the bracket in mid-arc, and is forced back from the contact, but never reaches its initial point, and each trip back after striking the bracket is smaller and smaller.
** Your description of the pendulum's motion from the 2d hit to 4th hit: **
Between the first hit and second hit, the motion differs between release and first hit, because the motion seems to be less arc-like, almost looking more like horizontal movement.
** 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 betwen release and second hit differs from the motion between second and fourth becuase there is less displacement and acceleration between the second and fourth hit compared to release and second 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: **
Less displacement, slower velocity, decreasing acceleration.
&#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 an appropriate response. Your response might be an answer to a question, a revision of your original response, or a question indicating what you do and do not understand about the situation along with a request for clarification. 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 you may use any title you wish.
&#
** Your conjecture as to why a clear difference occurs in some intervals vs. others: **
The first interval is shorter because its release is from an extreme point which helps it get more acceleration and velocity compared to subsequent intervals.
** What evidence is there that subsequent intervals increase, decrease or remain the same: **
Subsequent intervals would increase in time.
** What evidence is there that the time between 'hits' is independent of the amplitude of the swing? **
To me this shows that a pendulum's swig depends both on the length of the pendulum and its displacement.
** **
This won't be the case if the pendulum is positioned so that the rhythm of the strikes is regular. The period and frequency of a pendulum have almost no dependence on the amplitude (max displacement) of the motion.
75min
** **
I believe you accurately observed your system. However I don't think you've positioned the pendulum so as to achieve a constant rhythm. It will be important that you do so in any subsequent experiments which use this system. See my notes regarding this.
I did ask you to submit a response regarding one of the later questions about the motion of the pendulum. The original question in the lab asked
'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. In similar terms to those used here, describe the motion of the pendulum between release and the first 'hit'.'
You accurately described the behavior of the velocity and acceleration, but it's very important to also answer the question in the specified terms. This shouldn't take you more than a few minutes./h3>