Pendulum Swing

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:

1. Attach the pendulum bob to the string and suspend from the clamp stand so that the string is 100cm in length.

2. Set the pendulum swinging by displacing the bob through a small angle.

3. Time 20 swings of the pendulum. Record the data.

4. Repeat step 3 twice more recording the data each time.

5. Repeat steps 1 - 4 for different string lengths.

Results:

Length (cm) √Length

(cm) 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

Graph2

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