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Oscillating Mass

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Introduction

IB Physics Design Lab

Period of an Oscillating Mass

Joy Fan

International Baccalaureate

Sir Winston Churchill Secondary School

October 2, 2009

Period of an Oscillating Mass

1        Planning A

1.1        Research Question

The aim of this experiment is to predict how the mass of the oscillating object m and the elongation of the spring l will influence the period of an oscillating mass on a spring and devise an experiment to test that prediction.

1.2        Hypothesis

The oscillating mass comprises of a vertically-hanging mass on a spring. Physical quantities of the oscillating mass include mass m, length l of the elongation of the spring, the spring constant k, and the period T of the oscillating mass (which is the time it takes for the mass to swing through one complete oscillation). I am choosing to study the mass m of the object and the length l of the elongation of the spring because past experience and preliminary investigation lead me to believe that the period of the oscillating mass should have a direct relationship with these two factors.

The Second Law of Motion as proposed by Sir Isaac Newton states that the net external force on a body is equal to the mass of that body multiplied by its acceleration:

image00.png

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Middle

Repeat this process 3 times to obtain an average period T of one full         oscillation. Timing 10 periods lowers uncertainty.record length-period pair values for each length.

2. Repeat step 1 for the remaining lengths while making sure to keep the mass constant: 10cm, 15cm,         20cm, 25cm, 30cm, and 30cm. Record length-period pair values for each length. Observe whether the         spring is oscillating slower or faster.

2.3        Safety

  1. Swinging masses on springs are dangerous. Avoid getting hit by them during the experiment.
  2. Do not elongate the spring too much for small masses as the mass may swing out and pose a threat to         others.

3        Collection and Analysis of Data

3.1        Data Collection

Part I        Elongation of the spring: image19.png

Length of spring at equilibrium: image02.png

Data Table 1: Varying mass of oscillating object and raw period times of ten oscillations.

Mass of oscillating object in kg

(uncertainty in mass image03.png0.00001kg negligible)

Length of spring in cm after spring is hung image04.png

Time of ten oscillations, T (s) ± 0.1 s

Trail 1

Trail 2

Trail 3

0.400

25.55

6.0

6.1

6.1

0.600

30.50

7.9

7.8

7.8

0.800

35.55

8.8

8.8

8.7

1.00

41.05

9.9

9.8

9.7

1.20

45.50

10.7

10.6

10.5

1.40

50.55

11.3

11.3

11.4

1.60

56.00

11.3

11.7

11.8

Qualitative Observations made: The 1.60kg mass oscillates significantly slower than the 0.400kg. The ring stand also wobbled a little during the experiment, which is a source of uncertainty.

Data Processing:

Now in the following

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Conclusion

Obvious sources of error would include having tools that were difficult to measure precisely with, namely the meter stick and the stop watch, and also getting the spring to suspend symmetrically from one point. Also as I previously mentioned, the stop watch is only accurate to about one tenth of a second.

4.3        Improvements

Realistic improvements that could cut some weaknesses of the procedure could include using greater masses to obtain a larger range of results and doing the procedure in a greater space. The reason for this change would be to increase the time of oscillation because when we used smaller masses, often the time of the period was so short it was very difficult to start and stop the timer. If the period becomes slower and takes up more time, it could make timing more precise. Furthermore, more data points would increase the likeliness of an obvious correlation.

Moreover, I believe the more trials done, the better chance you will get of obtaining the best average value. The procedure itself is not that complicated, and I believe if I took the time to do 5-7 trials instead of just 3, the data would be more accurate. To improve the investigation I would also suggest using photo gates instead of stop watches to obtain time measurements more accurately and precisely.

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