Title
…Bifilar pendulum investigation
Aim
… To find the relationship between the lengths of suspension strings of a bifilar pendulum affects its
period
Independent variable – the length of the suspension swings
Dependent variable – the period of the pendulum (the time to swing from one side to the other and back again)
Control variables
1. The spacing between the strings must be kept the same (where they are attached to the ruler, and at the
top where they are suspended). I will use a spacing of 20cm, measuring from the centres of the string.
2. Use the same ruler for the experiment.
3. Use the same method for deflecting the ruler (twist at the centre of the ruler) and use a small deflection
each time (approximately 15˚)
Accuracy improvement
1. I will time 10 oscillations and divide by 10 to get the time for one period. This will reduce the effect of
random variations in my times.
2. I will reduce parallax error when measuring length by making sure I am viewing the scale at 90˚, and
making sure the ruler is close to the strings.
Method
1. Set up the equipment as shown in the diagram.
2. Adjust the spacing of the strings so they are 20cm apart (check at the top and bottom of the strings)
3. Adjust the length of the strings to 20cm
4. Check spacing of the strings is still 20cm apart (check at the top and bottom of the strings)
5. Hold the ruler at the centre and twist it (around 15˚) and let go
6. Time 10 oscillations and record the time
7. Repeat step 6 until 5 times are recorded.
8. Repeat steps 2 to 7 for lengths of 20, 40, 60 and
80cm
9. Process results to enable a relationship to be
worked out
suspension
cord
rod of length, r
D
axis of
rotation
L
horizontal
twist
Results
Processing
The unprocessed data above would not give a straight line graph.
As
 2r
T 
 D 3g


 L


T is proportional to √L, therefore I will need to graph T against √L to get a straight
line graph and work out the equation.
Graph on the next page
The absolute uncertainty values for √L are too small to plot on the scale that I have used on my graph
Gradient of best fit line
Rise = 5.9s
Run = 1.02 √m
Gradient = 5.9/1.02 = 5.784
Gradient of worst fit line
Rise = 5.9s
Run = 0.96 √m
Gradient = 5.9/0.96 = 6.145
Difference between gradient of best and worst fit line
Δgradient = 6.145 – 5.784 = 0.361 = 0.4 (1sf)
Gradient = 5.8 ±0.4
The relationship for the line is
T = (5.8 ±0.4) √L
2
Period v square root of length
7.00
6.00
Best fit line
Worst fit line
5.00
Period (s)
4.00
3.00
2.00
1.00
0.00
0.000
0.200
0.400
0.600
0.800
Square root length (√m)
3
1.000
1.200
Conclusion and Evaluation
For achieved level
In conclusion the period of the pendulum is related to the length of the strings by the formula
T = 5.8 √L
For Merit and Excellence level
In conclusion the period is related to the length of the strings by the formula
T = (5.8 ±0.4) √L
The uncertainty in the gradient is due to the uncertainties that I accounted for during the experiment and
processing of the data.
**********************************************************************************************************
Also for Merit

Evaluate the quality of the results e.g. effectiveness of accuracy improving techniques, any outliers, the
variation in the lines of best and worst fit, errors in the measured data that could have affected the graph
For Excellence

a discussion that shows critical thinking, evaluates and explains the validity of the results, and considers
relevant physics theory e.g. relate any errors to their effect on the results and link this to the effect on
the graph (such as altering the gradient), compare your equation to the given equation (work out the
value of g based on your equation) and comment on how this relates to the validity of your results.
The following information is from the TKI site http://www.tki.org.nz/r/ncea/physics3_1Cv1_23dec05.doc

statements that would be accepted as showing critical thinking. Such statements could include:
 a critical comparison of the experimental set up with the real life situation it is modelling and an
explanation of the limitations of the model.
 the identification of an uncontrollable variable and how it would have affected the measurements and
hence the results.
 a reason why the particular value for a controlled variable was chosen and the impact this choice would
have had on the reliability of the results. E.g. the resistance of a rheostat may have to be carefully
chosen so that a lamp does not exceed its maximum voltage but the current and voltage measurements
have a reasonable range.
 a description of a crucial aspect in the setting up of the experiment and an explanation of why the
aspect is crucial.
 a description of an unavoidable difficulty that was experienced in making a measurement and the
impact it would have had on the reliability of the results.
 a description of an unusual technique, probably specific to the measurement being carried out, that was
used to improve accuracy; why this technique was needed; and the impact its use would have had on
the reliability of the results.

statements that would be accepted as evaluating and explaining the validity of the results. Such statements
could include:
 if applicable, an explanation for the choice of the positioning of the best fit / error lines in terms of the
uncertainty in the plotted data.
 suggested explanations for how the experimental process could have brought about a gradient value (or
intercept value) that is more than / less than the expected value.

statements that would be accepted as consideration of relevant physics theory. Such statements could
include:
 a comparison of the theoretical value of a physical constant with the value calculated from the
experimental relationship (obtained by comparing the experimental equation with a given theoretical
equation) and an interpretation of the uncertainties in terms of the reliability of the conclusion.
 recognition that an unexpected axis intercept might arise from the presence of an unaccounted for
systematic error and suggestions as to how this error might have arisen.
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