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Question: Does the length of the string holding the pendulum in mid-air affect the frequency?

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Introduction

Factors that Affect the Frequency of a Pendulum

Friday, February 8th, 2011

Written By: Moiz Zahid

Performed with: Samer Hafuth and Milos Jovkovic

Question: Does the length of the string holding the pendulum in mid-air affect the frequency?

Hypothesis: If the length of the string is increased then the frequency of the pendulum will decrease.

Explanation: When the length of the string is increased, the frequency decreases as it takes more time for the pendulum to complete one cycle. The more time it takes the slower the movement meaning the lower the frequency. Since frequency equals number of cycles divided by total time, the larger the time amount the more the cycles are divided by, which would result in a smaller number. This is similar to water waves as the larger the wave the slower it moves and the lower its frequency.

Figure 1: Graph Sketch

image12.png

Variables:

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Middle

Repeat steps 3-9 for 30, 40 and 50cm string length (from C-Clamp to bottom of string loop), 4 times each, and 3 more times for 20cm length to get 4 trials for each length.

Observations:Table 1: Comparing String Length with Time

Trial

String Length (cm)

±0.01

Time (seconds)

±0.5

1

20

16.1

2

15.9

3

15.8

4

15.8

5

30

18.6

6

18.2

7

18.6

8

18.4

9

40

20.5

10

20.6

11

20.6

12

20.6

13

50

22.2

14

22.2

15

22.4

16

22.3

*Retort Stand wobbled throughout the experiment

Analysis:

Sample Calculation:image02.png

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Conclusion

        Second Source of Error is the pendulum clamp interference with string while it moves. Since the String is looped around the pendulum clamp holder, and swings perpendicular to the clamp, the clamp interferes with the movement of the string. As the string swings it hits the clamp near the rest position which causes the string to slow down in its movement. When the string slows down the time increases which causes inaccurate frequency measurement and inaccurate timing. This factor could be fixed by having a clamp where the string hangs below it and swings below it, so that there is no interference in the movement of the string.                

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