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# OCR B Advancing Physics Physics Practical Investigation Coursework Investigating Simple Harmonic Oscillations

Extracts from this document...

Introduction

Physics Practical Investigation Coursework

Investigating Simple Harmonic Oscillations

This investigation aims to explore the nature of different oscillating systems, including the factors upon which the oscillation depends and the energy transfer involved.

Preliminary Experiment

A pendulum was made using a bob hanging, by a piece of string, from a standing clamp. Experiments were carried out, recording the time taken for ten complete cycles from angles of displacement ranging from 5 to 30° in 5° intervals.  In separate experiments, the mass and string length were changed as the independent variables in order to investigate the effect they had upon the period of oscillation. The mass of the bobs used were 100, 200 and 300g; the length of the string varying between 15cm and 30cm. For each experiment, three trials were completed in order to allow identification of anomalous results and enable the calculation of an average time – this value was then divided by ten in order to work out the average time of one oscillation.

 Length of string: 0.15m Average time for 1 oscillation (s) Amplitude: Angle of initial displacement (degrees) 100g 200g 300g 5 1.08 1.08 1.09 10 1.08 1.09 1.09 15 1.09 1.09 1.09 20 1.08 1.09 1.08 25 1.09 1.10 1.09 30 1.09 1.10 1.09 Length of string: 0.3m Average time for 1 oscillation (s) Amplitude: Angle of initial displacement (degrees) 100g 200g 300g 5 1.31 1.32 1.31 10 1.32 1.33 1.32 15 1.32 1.33 1.32 20 1.32 1.33 1.33 25 1.33 1.33 1.33 30 1.33 1.34 1.33

For complete table of data, see appendix.

Middle

A source of error could be that the surface area of the hanging mass does not remain constant – meaning there could be additional friction between mass and fluid with larger masses and consequentially a greater loss of energy.

The effect of the damping can be seen more easily by comparison between the two experiments.

As can be seen in the graph, the resonant frequency is consistently lower in the damped system than in the undamped system.

 Mass (kg) Undamped Average ResonantFrequency (Hz) Damped Average ResonantFrequency(Hz) Difference (Hz) % Difference 0.10 2.57 2.00 0.57 22.08 0.15 2.38 1.80 0.58 24.48 0.20 2.12 1.65 0.47 22.05 0.25 2.00 1.45 0.55 27.50 0.30 1.90 1.39 0.51 26.67 0.35 1.80 1.31 0.49 27.41 0.40 1.70 1.23 0.47 27.45

The damping effect reduces the resultant frequency by an average of 0.52Hz. The percentage decrease in resonant frequency increases slightly with mass – possibly due a greater surface area of larger masses as discussed above.

To calculate an approximatepercentage change, where the lines of best fit are almost equal in gradient (0.4 and 0.44), the first point was removed. The intercepts differ by 7.92 meaning that, over this range of values, the amplitude is reduced by approximately 8cm by the damping effect of the water. As a percentage change this is:     (8/8.81) x 100 = 91%.

The reason that, in reality, the difference is not linear (especially in the undamped) system is the square relationship between amplitude and energy (E=1/2 kx2).

Conclusion

an>

Trial 2

Trial 3

Average

Average time for 1 oscillation

5

10.71

10.80

10.82

10.78

1.08

10

10.82

10.80

10.92

10.85

1.08

15

10.86

10.87

10.86

10.86

1.09

20

10.83

10.82

10.87

10.84

1.08

25

10.88

10.90

10.90

10.89

1.09

30

10.87

11.00

10.93

10.93

1.09

Length 15cm

Time taken for 10 oscillations

Mass 200g

Angle of initial displacement (degrees)

Trial 1

Trial 2

Trial 3

Average

Average time for 1 oscillation

5

10.74

10.84

10.89

10.82

1.08

10

10.90

10.93

10.95

10.93

1.09

15

10.89

10.84

10.90

10.88

1.09

20

10.84

10.93

11.01

10.93

1.09

25

10.98

11.00

10.93

10.97

1.10

30

11.02

11.02

11.02

11.02

1.10

Length 15cm

Time taken for 10 oscillations

Mass 300g

Angle of initial displacement (degrees)

Trial 1

Trial 2

Trial 3

Average

Average time for 1 oscillation

5

10.76

10.80

11.01

10.86

1.09

10

10.84

10.79

10.92

10.85

1.09

15

10.82

10.90

10.86

10.86

1.09

20

10.80

10.89

10.85

10.85

1.08

25

10.84

10.90

11.01

10.92

1.09

30

10.89

11.00

10.90

10.93

1.09

 Trial 1 Trial 2 Trial 3 Undamped Mass (kg) Resonant Frequency Amplitude of Resonant Frequency Resonant Frequency Amplitude of Resonant Frequency Resonant Frequency Amplitude of Resonant Frequency Average Resonant Frequency Average Amplitude of Resonant Frequency 0.10 2.60 5.00 2.60 5.50 2.50 5.50 2.57 5.33 0.15 2.40 9.50 2.40 9.00 2.35 9.00 2.38 9.17 0.20 2.10 10.00 2.15 10.20 2.10 10.60 2.12 10.27 0.25 2.00 10.20 2.00 10.50 2.00 11.20 2.00 10.63 0.30 1.90 10.90 1.90 11.20 1.90 11.25 1.90 11.12 0.35 1.80 11.00 1.80 11.40 1.80 11.30 1.80 11.23 0.40 1.70 11.20 1.70 11.30 1.70 11.45 1.70 11.32 Trial 1 Trial 2 Trial 3 Damped Mass (kg) Resonant Frequency Amplitude of Resonant Frequency Resonant Frequency Amplitude of Resonant Frequency Resonant Frequency Amplitude of Resonant Frequency Average Resonant Frequency Average Amplitude of Resonant Frequency 0.10 2.00 1.50 2.00 1.50 2.00 1.60 2.00 1.53 0.15 1.80 2.20 1.80 1.60 1.80 1.70 1.80 1.83 0.20 1.70 3.00 1.60 2.00 1.65 2.00 1.65 2.00 0.25 1.45 2.30 1.45 2.60 1.45 2.10 1.45 2.33 0.30 1.40 3.00 1.40 3.30 1.38 3.70 1.39 3.15 0.35 1.32 3.60 1.30 3.60 1.30 3.50 1.31 3.57 0.40 1.25 4.00 1.20 4.20 1.25 4.00 1.23 4.07

Anomalous results (in red) are not included in averages.

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