Pendulum Swing
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Graphical Analysis
Aim: To investigate, by graphical means, the relationship between periodic time and length for a simple pendulum.
Apparatus: Pendulum bob, light string, clamp stand, meter ruler, stopwatch, graph paper.
Theory: The relationship between two physical quantities can be determined by graphical means. For a simple pendulum, the relationship between periodic time and length is given by the equation
Where, T is the periodic time, 1 is the length of the pendulum string and g is acceleration due to gravity
A graph of periodic time against length should be of the shape shown.
Hypothesis: That the shorter you create the pendulum string, the shorter the time difference for a swing.
Method:
Attach the pendulum bob to the string and suspend from the clamp stand so that the string is 100cm in length.
Set the pendulum swinging by displacing the bob through a small angle.
Time 20 swings of the pendulum. Record the data.
Repeat step 3 twice more recording the data each time.
Repeat steps 1 – 4 for different string lengths.
Results:
Length (cm)
√Length
Trial 1
(secs)
Trial 2 (secs)
Trial 3 (secs)
Average Time
Periodic Time
142.8±0.1
11.950±0.01
49.37
47.97
47.97
47.73±0.48
2.3865±0.02
136.0±0.1
11.662±0.01
46.25
46.41
46.53
46.39±0.15
2.3195±0.01
130.6±0.1
11.428±0.01
46.06
45.75
45.68
45.83±0.23
2.2915±0.01
118.8±0.1
10.900±0.01
42.97
43.66
42.78
43.14±0.52
2.1570±0.03
97.9±0.05
9.894±0.01
39.10
39.40
39.20
39.23±0.17
1.9615±0.01
83.3±0.05
9.127±0.01
35.97
36.03
36.59
36.29±0.39
1.8145±0.02
57.6±0.05
7.589±0.01
30.32
30.67
30.47
30.49±0.18
1.5245±0.01
Graph 1
Graph2
Analysis:
The shape of Graph 1 suggests that the relationship between time and length is:
T√1
This relationship is confirmed in Graph 2, where by finding the square root of the length creates a straight-line