Equipment required:

      A 50 cm long pendulum (bob and string)                             Rigid support and stand

        Metre rule                                                                                  Stopwatch

Introduction                                                                                                                            rigid support

The period of a pendulum is defi ned as the time (in seconds) that the pendulum takes to make one complete oscillation (see page 15

in your textbook).                                                                                                                                 _string

To reduce the human error in determining when to start and stop           _simple the stop watch you must measure multiple periods, for example          pendulum 20 periods, and then divide your result by the number of periods               bob

measured. It is best to start and stop the watch when the pendulum        one completeswing is moving at its fastest, i.e. at the bottom of the swing as it is diffi cult to determine when the pendulum has stopped at its highest point.

Theory

For small angle oscillations the period, T, of a pendulum is given by:

__

T = 2π  √ _ gl   or T 2 =  4____πg2  l   

The length of the pendulum, l, is defi ned as the distance between the centre of mass of the bob and the pivot point. g is the acceleration due to gravity.

Plotting a graph of T ² against l should produce a straight line graph through the origin by comparing T ²

=  ^4____π_g^{2  l}  with the equation of a straight line:        y = mx + c. The slope of the graph is equal to ^{___ 4}_g^{π 2} . We can fi nd   a value for g by determining the slope of the T ² against l graph.

Method

1      Fix the length of the pendulum at 20 cm.

2      Draw the pendulum back such that the sting makes a small angle to the vertical. Release the bob and allow the pendulum to oscillate to and fro.

3      Start timing when the bob has passed through the lowest position a few times.

4      Stop timing when the bob has made 20 oscillations.

5      Record the time in the table below.

6      Repeat the experiment for the pendulum at 20 cm at least one more time, preferably twice.

7      Repeat the experiment for the different lengths of the pendulum given in the table below.

© OUP: this may be reproduced for class use solely for the purchaser’s institute

© OUP: this may be reproduced for class use solely for the purchaser’s institute