What factors influence the motion of a pendulum? How do those factors influence the motion of the pendulum?

Materials Used:

• Stop Watch x 1
• Weight (100gm)  x 6
• String in lengths of 25cm , 50 cm and 70 cm
• Tape
• Protractor
• Retort Stand
• Books

Method:

In this section there will three different methods due to the nature of our hypotheses.

Method 1: Changing the Length of the String

1. Setup the retort stand, place heavy books on the stand’s base so that it remains stable during movement of the pendulum.
2. Tie a string with length of 25cm to the stand.
3. Attach a 200gm mass to the string and let it hang
4. Test the setup by letting the mass from one side to the other. Make sure everything is tight.
5. Hold the mass 90 degree from the normal line
6. Start the stop watch as soon as it leaves your hand from the 90 degree mark
7. Stop the stopwatch when it is back in your hand on the same side.
8. Let the pendulum complete 1 cycle thus forward and backward.
9. Do this 5 times and then take an average.

10. Another way is to start the stopwatch and let the pendulum complete 5 cycles before stopping the stopwatch.
11. Repeat this experiment with string lengths of 50 cm and 75 cm

Method 2: Changing the Mass

1. Use the same Retort stand as above.
2. Use string length of 25cm and keep it constant throughout the experiment.
3. Start by attaching a mass of 200gm to the string.
4. Test the setup by letting the mass from one side to the other. Make sure everything is tight.
5. Hold the mass 90 degree from the normal line
6. Start the stop watch as soon as it leaves your hand from the 90 degree mark
7. Stop the stopwatch when it is back in your hand on the same side.
8. Do this 5 times and then take an average
9. Repeat the experiment with masses of 400gm and 600gm

Method 3 : Changing the Angle

1. Use the same Retort stand as above
2. Use string length of 25cm and a mass of 200gm and keep it constant throughout the experiment.
3. Hold the pendulum at 45 degrees and then let it complete 1 cycle.
4. Do this 5 times and then take an average
5. Repeat this with 10, 20, 30, 90 and 135 degrees.

Results:

The following table will represent the results which we recorded for the three different experiments.  The red values will indicate averages

Experiment 1: Changing the length of the string

The following table represent the results when we let the pendulum complete 5 cycles before taking the time

Experiment 2: Changing the Mass

Experiment 3: Changing the Angle

Data Presentation

The following graphs will illustrate the results, which I obtained.

Graph 1: Different String Lengths

Graph 2: Different Masses

                                                                                                         

Graph 3:  Different Angles

                                                                         

From the graphs above I can clearly see that there are variations in our results.

In the first graph I can see the pendulum with the smallest string had the shortest period.

The reason for this is because when there is a long string attached to the pendulum, then the pendulum has a much greater distance to cover before it can complete a  cycle. In other word I can refer to this that the arc length that needs to be covered by the pendulum is much greater when the string is long and little when the string is short.

The second graph represents the results I obtained from changing the masses. Form this graph I can see that the pendulum with the greatest weight had the shortest period.

This can be explained in terms of force. When the pendulum left my hand at an angle of 90 degree from normal, it went down with a lot of speed. The equation for Force can be used to explained. F= MA

.6 x 9.8 = 5.88 N

.4 x 9.8 = 3.92 N

.4 x 9.8 = 1.96 N

 From the calculations above I can see that the 600 gm had the greatest downwards force therefore it was able to move faster and complete a cycle faster.

The last graph illustrates the results , when we changed the angle from which we started the pendulum’s oscillation.

From the results I can identify that when the pendulum is started at 10 degree it will have the shortest period. This is because of the fact that the arc length of it’s cycle is not as long as with the other angles.

Conclusion:

After doing this experiment I was able to answer my predictions to all the experiments.

After comparing my hypotheses to my results I can see that my experimentation proves my hypotheses correct which was that a shorter string would have a shorter period.

My results also prove my hypotheses for the change of mass correct. I hypothesized that the heavier the mass the shorter the period. The results from changing the angle shows that my hypotheses for the angle experiment was incorrect and that it should actually be vice versa. From these experiments I am able to conclude that the shorter the arc length of a pendulum the sorter the period would be. I also learned that the period of the pendulum can depend on various factors, such as angle, mass and length of string.

Evaluation:

I feel that the method which we followed were extremely simple to follow. This enabled us to work accurately. I do however want to express the need for two people to do the angle experiment because it does get a bit tricky when you have to measure the angle hold the pendulum steady and still do the timing. I would also like to warn people about the possible parallax mistake they could make when making the readings.

Our results are accurate but I would like to do the angle experiment again because I feel that there might be some values which are incorrect due to the parallax mistake. I did look straight at the protractor but from an angle.

For further experimentation I would recommend people to use a swivel for the pendulum to swing on rather than a crossbar. This would eliminate traces of friction and will improve the accuracy of the results.

Bibliography

Pendulum",Microsoft® Encarta® Encyclopedia 2001. © 1993-2000 Microsoft Corporation.

        

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