The Pearl Pendulum

If the bracket is tilted back a bit, as shown in the next figure below, the pearl will naturally rest against the bracket.  Tilt the bracket back a little bit and, keeping the bracket stationary, release the pendulum. 

Listen to the rhythm of the sounds made by the ball striking the bracket.

• Do the sounds get closer together or further apart, or does the rhythm remain steady?   I.e., does the rhythm get faster or slower, or does it remain constant?
• Repeat a few times if necessary until you are sure of your answer.

Insert your answer into the box below, and give a good description of what you heard to make you sure of the answer.

The usual report is that when the bracket is tilted 'back' the sounds get closer together.

If the bracket is tilted forward a bit, as shown in the figure below, the pearl will naturally hang away from the bracket.  Tilt the bracket forward a little bit (not as much as shown in the figure, but enough that the pearl definitely hangs away from the bracket).  Keep the bracket stationary and release the pendulum.  Note whether the pearl strikes the bracket more and more frequently or less and less frequently with each bounce.

Again listen to the rhythm of the sounds made by the ball striking the bracket.

• Do the sounds get closer together or further apart, or does the rhythm remain steady?   I.e., does the rhythm get faster or slower, or does it remain constant?
• Repeat a few times if necesary until you are sure of your answer.

Insert your answer into the box below, and give a good description of what you heard to make you sure of the answer.

The usual report is that the sounds get further apart.

If the bracket is placed on a perfectly level surface, the pearl will hang straight down, just barely touching the bracket.  However most surfaces on which you might place the bracket aren't perfectly level.  Place the bracket on a smooth surface and if necessary tilt it a bit by placing a shim (for a shim you could for example use a thin coin, though on most surfaces you wouldn't need anything this thick; for a thinner shim you could use a tightly folded piece of paper) beneath one end or the other, adjusting the position and/or the thickness of the shim until the hanging pearl just barely touches the bracket.  Pull the pearl back then release it.

If the rhythm of the pearl bouncing off the bracket speeds up or slows down, adjust the level of the bracket, either tilting it a bit forward or a bit backward, until the rhythm becomes steady.

Describe the process you used to make the rhythm steady, and describe just how steady the rhythm was, and how many times the pendulum hit the bracket..

A variety of descriptions are generally given for how the bracket is tilted to just the right angle.  A common report is that this is achieved when the freely hanging ball, when it comes to rest, is just barely in contact with the bracket.

On a reasonably level surface, place one domino under each of the top left and right corners of your closed textbook, with the front cover upward.  Place the bracket pendulum on the middle of the book, with the base of the bracket parallel to one of the sides of the book.  Release the pendulum and observe whether the sounds get further apart or closer together.  Note the orientation of the bracket and whether the sounds get fuirther apart or closer together.

Now rotate the base of the bracket 45 degrees counterclockwise and repeat, being sure to note the orientation of the bracket and the progression of the sounds.

Rotate another 45 degrees and repeat.

Continue until you have rotated the bracket back to its original position.

Report your results in such a way that another student could read them and duplicate your experiment exactly.  Try to report neither more nor less information than necessary to accomplish this goal.  Use a new line to report the results of each new rotation.

The usual report indicates that at some specified angles the rhythm 'speeds up' and at others the rhythm 'slows down', while at certain other angles the rhythm remains constant.

Describe how you would orient the bracket to obtain the most regular 'beat' of the pendulum.

**

Orient the bracket in this position and start the TIMER program.  Adjust the pendulum to the maximum length at which it will still bounce regularly.

Practice the following procedure for a few minutes:

Pull the pendulum back, ready to release it, and place your finger on the button of your mouse. Have the mouse cursor over the Click to Time Event button. Concentrate on releasing the pendulum at the same instant you click the mouse, and release both.  Do this until you are sure you are consistently releasing the pendulum and clicking the mouse at the same time.

Now you will repeat the same procedure, but you will time both the instant of release and the instant at which the pendulum 'hits' the bracket the second time.  The order of events will be:

• click and release the pendulum simultaneously
• the pendulum will strike the bracket but you won't click
• the pendulum will strike the bracket a second time and you will click at the same instant

We don't attempt to time the first 'hit', which occurs too quickly for most people to time it accurately.

Practice until you can release the pendulum with one mouse click, then click again at the same instant as the second strike of the pendulum.

When you think you can conduct an accurate timing, initialize the timer and do it for real.  Do a series of 8 trials, and record the 8 time intervals below, one interval to each line.  You may round the time intervals to the nearest .001 second.

Starting in the 9th line, briefly describe what your numbers mean and how they were obtained.

If the pendulum has been set up so that the rhythm remains constant, then the actual time intervals should be very consistent.  However due to the fact that the 'triggering' of the mouse is done by a human observer, there will be some degree of inconsistency in these measurements.  Each individual will also have a tendency to time either a little short or a little long; with training this tendency can be reduced, but never eliminated.

Finally, you will repeat once more, but you will time every second 'hit' until the pendulum stops swinging.  That is, you will release, time the second 'hit', then time the fourth, the sixth, etc..

Practice until you think you are timing the events accurately, then do four trials.

Report your time intervals for each trial on a separate line, with commas between the intervals.  For example look at the format shown below:

.925, .887, .938, .911

.925, .879, .941

etc.

In the example just given, the second trial only observed 3 intervals, while the first observed 4.  This is possible.  Just report what happens in the box below.  Then on a new line give a brief description of what your results mean and how they were obtained.

If the pendulum has been set up so that the rhythm remains constant, then the actual time intervals, starting with the interval from the second to the fourth 'hit', should be very consistent.  Even with 'human' triggering there should be very little overall tendency for the intervals to get shorter or longer with subsequent 'hits'.

Now measure the length of the pendulum.  (For the two-pearl system the length is measured from the bottom of the 'fixed' pearl (the one glued to the top of the bracket) to the middle of the 'swinging' pearl.  For the system which uses a bolt and magnet at the top instead of the pearl, you would measure from the bottom of the bolt to the center of the pearl).  Using a ruler marked in centimeters, you should be able to find this length to within the nearest millimeter.

What is the length of the pendulum?

****

If you have timed these events accurately, you will see clearly that the time from release to the second 'hit' appears to be different than the time between the second 'hit' and the fourth 'hit'.

On the average,

• how much time elapses between release and the second 'hit' of the pendulum,
• how much time elapses between the second and fourth 'hit' and
• how much time elapses between the fourth and sixth 'hit'?

Report your results as three numbers separated by commas, e.g.,

.63, .97, .94

If the pendulum has been set up so that the rhythm remains constant, then the actual time intervals, starting with the interval from the second to the fourth 'hit', should be very consistent.  Even with 'human' triggering there should be very little overall tendency for the intervals to get shorter or longer with subsequent 'hits'.

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.

How many intervals from extreme point to equilibrium, or from equilibrium to extreme point, occur between release and the first 'hit'?

Student frequently describe the motion in terms of how far the pendulum swings, and it is common for students to report that because the swings get shorter, the 'hits' get closer together.  Note first that the subsequent 'hits' won't get closer together if the rhythm is constant. 

However, the question asked here is about how many intervals occur.  From release to first 'hit' we have one interval from extreme to equilibrium.

Describe the motion of the pendulum between the first 'hit' and the second 'hit', and explain how this motion differs from the motion between release and the first 'hit'.

From release to first 'hit' we have one interval from extreme to equilibrium; from first 'hit' to second 'hit' we have one interval from equilibrium to extreme, then one interval from extreme to equilibrium.  This makes a total of three such intervals from release to first 'hit'.