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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 3.80s ± 0.02s 0.20 4.59s ± 0.02s 0.30 5.80s ± 0.02s 0.40 6.58s ± 0.02s 0.50 7.57s ± 0.02s

Uncertainty for calculating average time taken

(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 0.76s ± 4.03x10-3s 0.20 0.92s ± 4.88x10-3s 0.30 1.16s ± 6.15x10-3s 0.40 1.32s ± 6.97x10-3s 0.50 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 The period of the pendulum could be calculated with the formula; 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        20.63% 0.20m±0.01m 0.90s±0.045s 0.92s ± 4.88x10-3s        2.22% 0.30m±0.01m 1.10s±0.037s 1.16s ± 6.15x10-3s        5.45% 0.40m±0.01m 1.27s±0.032s 1.32s ± 6.97x10-3s        3.94% 0.50m±0.01m 1.42s±0.028s 1.51s ± 8.02x10-3s        6.64%

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.

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

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