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 and the bouncing stops after just a few seconds, with the ball resting against the bracket.
** Your description of the rhythm of the pendulum when tilted 'forward' **
The sounds get further apart. After the sound stops, the ball continues to swing but not hard enough to make contact with the bracket.
** Your description of the process used to keep the rhythm steady and the results you observed: **
The ball struck the bracket 21 times. I shimmed the bracket with two folds of a sandwich bag that came with the lab kit.
** Your description of what happened on the tilted surface (textbook and domino), rotating the system 45 degrees at a time: **
For the report, zero degrees rotation is the starting point with the bracket at the steepest angle and the end with the pearl on the upward incline. Each data record will include an angle of rotation, number of strikes, and 'faster' or 'slower' to indicate the rhythm of the pearl striking the bracket over time. Each observation was made with the pendulum dropped from the same distance, with the center approximately 2 from the bracket.
Deg Qty Rhythm
----------------------
0 18 Faster
45 16 Moderately faster
90 27 Steady
135 20 Moderately slower
180 12 Slower
215 15 Moderately slower
270 19 Steady
315 14 Faster
** Your description of how you oriented the bracket on the tilted surface to obtain a steady rhythm: **
I would orient the bracket with the base horizontal.
** Your report of 8 time intervals between release and the second 'hit': **
0.660
0.660
0.539
0.621
0.590
0.539
0.660
0.664
0.691
0.691
0.633
These were obtained in the method described above. This time is the interval between the release of the pendulum and the second strike against the bracket. There is some error in the release method and synchronizing the timer with the strike, and energy losses in our system. The number represents the amount of time it takes for the pendulum to travel from the highest point in its arc to the lowest twice.
** Your report of 4 trials timing alternate hits starting with the second 'hit': **
1: 0.680, 0.621, 0.543, 0.551, 0.551, 0.551, 0.570. x-bar = 0.581
2: 0.594, 0.609, 0.531, 0.551, 0.570, 0.531, 0.570. x-bar = 0.565
3: 0.570, 0.590, 0.551, 0.563, 0.551, 0.590, 0.512, 0.540, 0.602. x-bar = 0.536
4: 0.598, 0.594, 0.539, 0.570, 0.551, 0.543, 0.598, 0.574, 0.590. x-bar = 0.573
x-bar-bar = 0.570
With the same opportunities for error in the previous set of data, this data shows that the period remains relatively constant while the amplitude decreases in each trial.
** The length of your pendulum in cm (you might have reported length in mm; the request in your instructions might have been ambiguous): **
87mm
** Your time intervals for alternate 'hits', starting from release until the pendulum stops swinging: **
0.052, 0.25, -0.071
I"ll bet these are the differences between the time intervals rather than the time intervals, which according to your resport are around .5 or .6 seconds.
** Your description of the pendulum's motion from release to the 2d hit: **
The motion of the pendulum between the release and the first hit is the motion from the extreme point to equilibrium.
That is correct for release to the first hit; what about release to 2d hit?
I see that you've given a good answer to this question below.
** Your description of the pendulum's motion from the 2d hit to 4th hit: **
Between the first and second hit, the pendulum travels from equilibrium to its extreme point back to equilibrium, twice the travel of the pendulum between release and the first hit.
** 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: **
release to second hit is a shorter travel distance and time than second to fourth hit. release to the second hit is from an extreme point to equilibrium (first hit) to an extreme point and back to equilibrium (second hit). second hit to fourth hit is from equilibrium (second hit) to extreme to equilibrium (third hit) to extreme to equilibrium (fourth 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: **
motion between second and fourth hit are the same as between fourth and sixth intervals.
** Your conjecture as to why a clear difference occurs in some intervals vs. others: **
First should be shorter because there is 25% less travel. I would contend that the error in synchronizing the release of the pendulum with the start of the timer could overcome the gain that should be seen by the shorter travel.
The typical user can synchronize, within .01 second or less, the release of the pendulum with the click of the mouse.
** What evidence is there that subsequent intervals increase, decrease or remain the same: **
subsequent intervals should stay the same if there were no system losses.
** What evidence is there that the time between 'hits' is independent of the amplitude of the swing? **
The experiment should show that the interval remains the same while the amplitude decreases.
** **
90 minutes. Had trouble finding all the lab pieces.
The wire is small and possible to overlook (which is why I included two in most kits).
** **
Very good work, though the data do not apprear consistent with (valid) theoretical predictions.
According to your description of the motion of the pendulum, release to 2d 'hit' should have taken only 3/4 the time between alternate subsequent 'hits'. Your data do not confirm this. No need to respond at this point, but you should think about why this was not observed (with good accuracy this is indeed what would be observed).