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To find the value of acceleration due to gravity by recording number of oscillations of a simple pendulum

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Introduction

Aditya Sareen

HL 1

Physics Lab 9

To find the value of acceleration due to gravity by recording number of oscillations of a simple pendulum

Satish Ahuja

XII-A

Physics HL 2

Raw Data

Meter Rule: Least count = 0.1 cm, uncertainty = 0.05cm

Vernier Calipers: Least count = 0.1cm, uncertainty = 0.05cm

Stopwatch: Least count = 1s, uncertainty = 0.5s

Table 1 – DATA9

Sr. No.

Length of string, l ± 0.05/cm

Time for oscillation, t ± 0.05/s

1

20

  1. 9.5
  2. 9.7
  3. 9.4
  4. 9.5

V.    9.3

2

40

  1. 12.3
  2. 12.4
  3. 12.7
  4. 12.6

V.    12.9

3

60

  1. 15.4
  2. 15.5
  3. 15.7
  4. 15.5

V.    15.1

4

80

  1. 18.7
  2. 18.6
  3. 18.7
  4. 18.7
  5. 18.4

5

100

  1. 21.4
  2. 21.4
  3. 21.8
  4. 21.5
  5. 21.8

6

120

  1. 25
  2. 25.1
  3. 25.3
  4. 25.3
  5. 25.4

7

140

I.      28.3

II.     28.5

III.    28.7

IV.    28.7

V.     28.4

  • The length of the string does not include the diameter of the bob 3.4 ± 0.05 cm)
  • The number of oscillations = 10

Data Processing

Uncertainty Calculation

  • The uncertainty of the ruler (± 0.05 cm) and half the uncertainty of the Vernier Caliper  (± 0.05/2 = 0.025)
  • Half of the uncertainty for the Vernier Caliper has to be taken as we have the diameter of the steel bob, and need only its radius.
  • The example calculation for the length of string  0.2m is shown below:
...read more.

Middle

Similarly, the calculations were performed for other readings

  • An average of the time values(in s) for each reading was taken
  • The calculation for the average time for string of length 20 cm is shown below:

Calculation 2

image02.png

Averaging the uncertainties:

image03.png

Therefore, our final answer stands as:

9.5 ± 0.5s

Rest of the calculations have been noted in the table below

Table 1.2 – Total Length and Average time for 10 oscillations

Sr. No

Total Length, n ± 0.525/cm

Average Time period for 10 oscillations, t± 0.5/s

1

20

9.5

2

40

12.44

3

60

15.54

4

80

18.68

5

100

21.6

6

120

25.22

7

140

28.52

  • We then convert the time period for 10 oscillations to the time period for just one oscillation
  • An example calculation using unitary method for the 1st time period is shown below

Example Calculation 3

image04.png

...read more.

Conclusion

Because the string was roughly tied around its support, the oscillations of the bob were haphazard and all over the place. These unnatural oscillations constitute a systematic error, and once again lead to either higher or lower readings for the value of time periodBecause the time period for one oscillation was too hard to measure, instead, the time period for 10 oscillations was taken. Multiple readings were taken, and averaged out to reduce errorThe base of the holder was uneven, and could lead to unnatural oscillations, which constitute a systematic error, and once again lead to either higher or lower readings for the value of time period

Aspect 3

  • A proper apparatus with a rigid support to suspend the string, along with an attached tape measure would reduce the random and systematic errors in this experiment
  • More number of readings could be taken, and averaging them would negate most of the random errors in this experiment
...read more.

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