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Investigate the effect of changing the length of a pendulum on the period of oscillation of the pendulum.

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Introduction

Physics Term 2 Internal Assessment

DCP & CE

Investigate the effect of changing the length of a pendulum on the period of oscillation of the pendulum.


                Table 1. Equipments and Uncertainties

Equipments

Uncertainties

Meter ruler

±0.01m

Electronic balance

±0.02g

Protractor

±0.50°

Stop Watch

±0.02s

Results:

        Table 2. Raw Data        

Lengths (m±0.01m)

Trial 1 (sec±0.02s)

Trial 2 (sec±0.02s)

Trial 3 (sec±0.02s)

Trial 4 (sec±0.02s)

Trial 5 (sec±0.02s)

Trial 6 (sec±0.02s)

Trial 7 (sec±0.02s)

0.10m

3.84

3.78

3.79

3.81

3.78

3.80

3.81

0.20m

4.59

4.65

4.57

4.62

4.60

4.61

4.59

0.30m

5.80

5.84

5.82

5.81

5.79

5.77

5.80

0.40m

6.60

6.50

6.62

6.63

6.63

6.56

6.53

0.50m

7.56

7.50

7.62

7.60

7.55

7.58

7.60

        Table 3. Average time taken for Each Lengths of Wire        

Length (m±0.01m)

Calculation

Average

0.10

image00.png

3.80s ± 0.02s

0.20

image01.png

4.59s ± 0.02s

0.30

image08.png

5.80s ± 0.02s

0.40

image12.png

6.58s ± 0.02s

0.50

image17.png

7.57s ± 0.02s

        Uncertainty for calculating average time taken

        Adding absolute uncertainties

        (3.84±0.02)+(3.78±0.02)+(3.79±0.02)+(3.81±0.02)+(3.78±0.02)+(3.80±0.02)+(3.                81±0.02)

        = (3.84+3.78+3.79+3.81+3.78+3.80+3.81) ± 7(0.02)

        = 26.62±0.14

        Dividing absolute uncertainties

              (26.62±0.14)/7        = (26.62±0.53%)/7

                                = 3.80±0.53%

                                = 3.80s ± 0.02s

        Table 4. Time Taken per Period

Length (m±0.01m)

Calculation

Time taken per period

0.10

image22.png

0.76s ± 4.03x10-3s

0.20

image29.png

0.92s ± 4.88x10-3s

0.30

image33.png

1.16s ± 6.15x10-3s

0.40

image38.png

1.32s ± 6.97x10-3s

0.50

image41.png

1.51s ± 8.02x10-3s

        Uncertainty for calculating period

              (3.80s±0.02s)/5        = (3.80±0.53%)/5

                                = 0.76±0.53%

                                = 0.76s ± 4.03x10-3s

        Graph 1. Period per Length

image02.png

        The period of the pendulum could be calculated with the formula;

image03.png

...read more.

Middle

1.10s±0.037s

0.40

T = 2 x pi x (0.40/9.81)1/2

   = 1.26874

1.27s±0.032s

0.50

T = 2 x pi x (0.50/9.81)1/2

   = 1.41850

1.42s±0.028s

        Uncertainty for theoretical value of the period

        Multiplying and dividing absolute uncertainties

              T        = 2 x pi x (0.10/9.81)1/2

        = 2 x pi x (0.10m±0.01m/9.81)1/2

                = 2 x pi x (0.10±10%/9.81)1/2

                = 2 x pi x (0.0102±10%)1/2

                = 2 x pi x (0.1±10%)

                = 0.63±10%

                = 0.63s±0.063s

        Table 6. Comparing the Gained Data and Theoretical Data

Lengths

Theoretical Data

Gained Data

Calculation

Difference

0.10m±0.01m

0.63s±0.063s

0.76s ± 4.03x10-3s

image04.pngimage04.pngimage05.pngimage05.png

image06.pngimage06.png

image07.pngimage07.png

20.63%

0.20m±0.01m

0.90s±0.045s

0.92s ± 4.88x10-3s

image04.pngimage04.pngimage09.pngimage09.png

image10.pngimage10.png

image11.pngimage11.png

2.22%

0.30m±0.01m

1.10s±0.037s

1.16s ± 6.15x10-3s

image04.pngimage04.pngimage13.pngimage13.png

image14.pngimage14.png

image15.pngimage15.png

5.45%

0.40m±0.01m

1.27s±0.032s

1.32s ± 6.97x10-3s

image04.pngimage04.pngimage16.pngimage16.png

image18.pngimage18.png

image19.pngimage19.png

3.94%

0.50m±0.01m

1.42s±0.028s

1.51s ± 8.02x10-3s

image04.pngimage04.pngimage20.pngimage20.png

image21.pngimage21.png

image23.pngimage23.png

6.64%

...read more.

Conclusion

Inaccurate measure of the wire

Different period of oscillations gained compared to the theoretical value

Use a clamp to hold on to the top of the wire and draw the line on the bottom of the wire and tie to the mass and make one person performing this part of the experiment to reduce systematic error

Reflex timing

Human cannot react right on time therefore error created in measuring the time taken for 5 oscillations

Repeat the trials more in order to dislocate the unreliable data and only use reliable data

Force given to the mass

Increases the velocity of the mass which affects the time taken for 5 oscillations

Repeat the trials more in order to dislocate the unreliable data and only use reliable data and make one person in order to reduce systematic error

Releasing the mass and creating different trend in oscillations

If the swinging trend forms a elliptical shape, then the time taken for 5 oscillations will be different to swinging trend forming a straight line

Repeat the trials more in order to dislocate the unreliable data and only use reliable data and make one person carry out to reduce random and systematic error.

...read more.

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