To observe how, the length and amplitude of a pendulum string, affect the time period for one oscillation. Prediction - I predict that the length

Variables: For amplitude as a factor.

Independent variable – I am changing the amplitude (angle of release.)

Dependent variable – I will be recording the time taken for 10 oscillations.

Control – Length of string (50cm), mass of bob (34.7g), gravitational constant (Earths gravitational pull) and type of string.

        

Apparatus:

• Cork.
• Stopwatch.
• Bob.
• String.
• Scissors.
• Clamp stand.
• Protractor.
• Metre ruler.
• Top pan balance.

Method: For length

1. Use the ruler to measure approximately 10cm of string. Leave a few centimetres extra, as you are required to tie it, this will compensate for the extra string need to tie a knot.
2. Cut the string at the selected measurement.
3. Set up the clamp stand.
4. Tie the bob to the string.
5. Use the scissors to slit the cork half way from the edge to the centre.
6. Fit the protractor inside the slit, so that it is secure firmly.
7. Place the cork onto the clamp making sure everything is intact.
8. Tie the other end of the string to the clamp.
9. Ensure that you line up the string on the 0° point on the protractor.
10. Take hold of the bob and extent the string it to its full length firmly.
11. Raise the bob to the side aligning it to the 10° point on the protractor.
12. Let go of the bob, as soon as you do this start the stopwatch.
13. Allow 10 oscillations to complete, at this moment stop the stopwatch and record your findings. (An oscillation is when the bob fully returned to its stating point once you have let it go.)
14. Repeat these steps again. Except increase the length of the string each time by 10cm until cm. E.g. 20cm, 30cm, 40cm, 50cm, 60cm.
15. Once the results have been collected and recorded. You will be able to calculate the time period for one oscillation from the average time period. This can be done by dividing the average time period by 10.

Method: for Amplitude

1. Use the ruler to measure approximately 10cm of string. Leave a few centimetres extra, as you are required to tie it, this will compensate for the extra string need to tie a knot.
2. Cut the string at the selected measurement.
3. Set up the clamp stand.
4. Tie the bob to the string.
5. Use the scissors to slit the cork half way from the edge to the centre.
6. Fit the protractor inside the slit, so that it is secure firmly.
7. Place the cork onto the clamp making sure everything is intact.
8. Tie the other end of the string to the clamp.
9. Ensure that you line up the string on the 0° point on the protractor.
10. Take hold of the bob and extent the string it to its full length firmly.
11. Raise the bob to the side aligning it to the 10° point on the protractor.
12. Let go of the bob, as soon as you do this start the stopwatch.
13. Allow 10 oscillations to complete, at this moment stop the stopwatch and record your findings. (An oscillation is when the bob fully returned to its stating point once you have let it go.)
14. Repeat these steps again. Except increase the amplitude of the string each time by 10° until 70°. E.g. 10°, 20°, 30°, 40°, 50°, 60°, 70°.
15. Once the results have been collected and recorded. You will be able to calculate the time period for one oscillation from the average time period. This can be done by dividing the average time period by 10.

Results:

Length as a factor

Cross sectional area as a factor – 50cm (fixed length)

 

Note: You should use these results to determine what the control will be for amplitude in the length factor, or what the control for length will be in the amplitude factor. As I will be investigating length, I have decided that I will use an amplitude of 30° and I think it is a suitable control, with regard to my preliminary results.

Conclusion

After carrying out my experiment I have found that as you increase the length of the pendulum string the time period for one oscillation increases and when you decrease the length the time period for one oscillation decreases. In addition that as you increase the amplitude the time period for one oscillation increases and as you decrease the amplitude the time period for one oscillation decreases. I was correct in my prediction which stated that the length of the pendulum string is directly proportional to the time period of one oscillation. Also, that the amplitude of the string is directly proportional to the time period. I.e. if I double the length the time period doubles and if I double the amplitude the time period doubles.

This is backed up on the scientific theory that if the pendulum is raised at a greater angle it will have to cover a greater distance. Also, the scientific theory backing up the length is Galileo’s findings in which he came up with the formula:

T = 2π √ L/g

This formula has only two values which are not constant, time and length. Hence, length and time are directly proportional, this supports my prediction.  I don’t think that there were any mistakes made in the experiment apart from minor measurements. I tired to be as accurate as I could. I used a metre ruler although it was very hard to measure the string with a meter ruler. Sometimes it was difficult to use a protractor to measure the amplitude as accuracy is hard to attain. My method was a suitable method for conducting this particular type of experiment and investigation. To improve the experiment I would have used a wider range of readings and I would have been able to see the limit I could reach with the length and amplitude. This way I could have better results and they could support my prediction more, even though it did. I would have also liked to investigate how the mass of the bob affects the time for one oscillation.