# Pendulum Swing

Topics: Pendulum, Bob, International System of Units Pages: 3 (623 words) Published: February 24, 2007
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 TimePeriodic Time 142.8±0.111.950±0.0149.3747.9747.9747.73±0.482.3865±0.02 136.0±0.111.662±0.0146.2546.4146.5346.39±0.152.3195±0.01 130.6±0.111.428±0.0146.0645.7545.6845.83±0.232.2915±0.01 118.8±0.110.900±0.0142.9743.6642.7843.14±0.522.1570±0.03 97.9±0.059.894±0.0139.1039.4039.2039.23±0.171.9615±0.01 83.3±0.059.127±0.0135.9736.0336.5936.29±0.391.8145±0.02 57.6±0.057.589±0.0130.3230.6730.4730.49±0.181.5245±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 graph for which we can confirm the mathematical equation in the theory section.