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# Motion of a Pendulum IB 10

Extracts from this document...

Introduction

Ankit Shahi                                                                                                          February 5 2009

Motion of a Pendulum

Design (D)

Aspect 1:

## Problem: How does length affect the period of a pendulum and what mathematical relationship is there between length and the period?

Variables:

• Manipulated : length
• Responding : frequency
• Controlled: string, room temp., angle that the pendulum is released and weight during examining the effects of length.

All these controlled variables were controlled by keeping the same bob and the same string. room temp. was also kept constant.

Aspect 3:

Materials: As per lab manual

Procedure: As per lab manual

Data Collecting and Processing (DCP):

Aspect 1:

 Length and motion of a pendulum ( Evidence ) 20 Length of pendulum ( +/- 0.001m) Angle of deflection ( +/- 1 ) Time for trial 1 ( +/- 0.005s) Time for trial 2 ( +/- 0.005s) 1.000 20 19.400 19.020 0.800 20 18.440 18.110 0.600 20 15.750 15.850 0.400 20 12.800 12.800 0.200 20 9.310 9.100
 Angle Changing ( Evidence ) 30  and 10 Angle of deflection ( +/- 1 ) Length of pendulum ( +/- 0.001m) Time for trial 1 ( +/- 0.005s) Time for trial 2 ( +/- 0.005s) 30 20 9.150 9.140 10 20 8.980 8.950

Aspect 2:

1.

Middle

Length and Motion of a pendulum ( Analysis )

Length of pendulum ( +/- 0.001m)

Angle of deflection ( +/- 1 )

Time for trial 1 ( +/- 0.005s)

Time for trial 2 ( +/- 0.005s)

Period Average ( +/- 0.01s)

Error for Period average

1.000

20

19.400

19.020

19.21

0.01

0.800

20

18.440

18.110

18.28

0.01

0.600

20

15.750

15.850

15.80

0.01

0.400

20

12.800

12.800

12.80

0.01

0.200

20

9.310

9.100

9.21

0.01

 Average of One period (+/- 0.0005s) Error for average of one period Frequency ( +/- 0.0001Hz) Error for frequency Period (T2) ( +/- 0.002s2) Error for T2 1.9210 0.0005 0.5206 0.0001 3.690 0.002 1.8275 0.0005 0.5472 0.0001 3.340 0.002 1.5800 0.0005 0.6329 0.0002 2.496 0.002 1.2800 0.0005 0.7813 0.0003 1.638 0.001 0.9205 0.0005 1.0864 0.0006 0.847 0.001 Angle Changing ( Analysis) Angle of deflection ( +/- 1 ) Length of pendulum ( +/- 0.001m) Time for trial 1 ( +/- 0.005s)

Conclusion

2 / m). Gravitational acceleration was calculated from the slope of the graph 10.01 m s-2 and if theoretical gravitational acceleration is taken 9.81 m s-2, relative error was found from that formula which was (2.01%)

There were some problems done during the experiment which caused the relative error to increase. Stopwatches were used that do not have uncertainty interval. Reaction time is also other error factor.  Flexibility of the string is a problem, non-flexible string was chosen but a change in the length of the string might cause error.

There were not any other errors caused by the apparatus. It was stable enough for the experiment. Therefore, there is no need to change the apparatus if this experiment would be done again. However, some other materials could be used such as the computer/multimedia system and a photo gate timer, to measure the period of the pendulum. They would decrease the relative error. Making the experiment in air vacuumed place will decrease the air friction.

This student written piece of work is one of many that can be found in our International Baccalaureate Physics section.

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