EXPERIMENT MODULE 4

Oscillatory Motion and Waves

A) The Simple Pendulum

Aim of the experiment

1.      In this experiment you are asked to investigate the factors that influence the periodic time of oscillation of a simple pendulum.

Aims for student learning

1.      To acquire the skill of determining an error from a range of values.

Theory

You might assume that the period of a pendulum depends upon the following factors:

(a)    The length, L, as measured from the point of suspension to the centre of gravity of the bob,

(b)    The mass of the bob, m

(c)    The starting angle, A, in radians (2 radians = 360°).

That is, that the period is some unknown function T = F(L,m,A). In order to empirically determine this function, it is necessary to keep two of the three variables (L, m and A) constant in turn while the third is varied and the corresponding values of T are observed.

To obtain a sufficiently accurate value of T, it is necessary to measure the time for a number of complete oscillations (10 perhaps) and by division obtain the time of one oscillation. Repeat each measurement at least 5 times and compute an average value. The largest difference between this average value and the actual values is the error. The error in the measurement of T must be calculated so that variations in the values obtained during the experiment can be assessed as either being significant or falling within the range of experimental error.

Equipment Needed

·        Length of fishing line or strong cotton

·        Several known masses to act as the pendulum bob e.g. coins on their own or taped together

·        Something to tie the pendulum to so it can swing freely e.g. a broom handle resting on the back of 2 chairs

·        Stop watch or the second hand of clock, or some other rhythmic time keeping device

·        Tape measure or ruler

·        Protractor http://www.ossmann.com/protractor/

Procedure and Results

Observations

• Begin your experiment by noting down the date as well as any peripheral information which may be relevant
• Before using any apparatus make sure that all the conditions are noted, so that you can exactly reproduce the experiment.
• A photograph or diagram would be useful

Data Collection

1.       By now you should understand how to design an experiment. Firstly though I would urge you to do a quick qualitative investigation to see which of the three variables, length, mass or starting angle has the greatest effect on the period of a pendulum. If more than one variable has an affect choose the one that has the most significant effect and keep the other variables constant.

2.       Quantitatively investigate how your chosen variable affects the period of a pendulum. Remember to do several trials at each value to reduce random error. Attach your graphs and tables to your report

Analysis

Calculations

1.      Use a spreadsheet to graph your results in such a way that the trendline helps you determine the relationship between the period and the variable you are investigating. You might like to try graphing T2 against L for instance.

2.      Plot your data with their associated with error bars.

3.      From this one graph of all of your data it should be possible to use the gradient of the graph to determine the acceleration due to gravity. (Do not find the value of g for each different length of the pendulum)

Discussion

·        Within experimental error what does the period of a pendulum depend upon?

·        Is your calculated value of g exactly 9.8 m/s2. If not why do you think this is so?

Conclusion

• How well do your results for experiment agree with the expected results?
• Briefly outline the reasons for the difference.

Extension to the experiment – this is not optional

The resonant frequency of a pendulum is 1/period i.e. Hertz or cycles per second. Investigate, just to an order of magnitude, the resonant frequency of several oscillating objects e.g. swing, leg when walking, nodding dog toy usually found in the back of cars.