The simple pendulum and the dependence of swing period on length

Secondary School Science Teaching Methods

INTRODUCTION

A simple pendulum consists of a mass hanging at the end of some massless (at least in theory) hanging device which is suspended from some pivot point.  In this laboratory exercise, you will determine the relationship between a simple pendulum’s length and its period (the time it takes for the pendulum to go back and forth).

MATERIALS

C  string

C  washers

C  paper clips

C  tape

C          a stop watch

C          a ruler or meter stick

PROCEDURE

1.    Obtain a length of string that is slightly more than 0.4 meter long.  On one end, attach a paper clip that is unfolded slightly, so that washers can be hung from the paper clip at the end of the string.

2.    Secure the opposite end of the string (the end without the paper clip) to a pen or pencil by wrapping it around a few times.  Do this so that the measurement between the pencil/pen and the center of where a washer will hang is exactly 0.40 meter.  You can secure the string with tape; and you can also secure the pencil/pen to a table using the same tape.

3.    Hang two (2) washers from the paper clip and pull the pendulum back a distance of 10.0 cm from the vertical orientation (where the pendulum naturally “wants” to hang). Time how long it takes the pendulum to swing back-and-forth (one complete period) 5 times.  Record this time in the table below.

4.    Repeat this procedure, filling in the rest of the table.  Remember to keep two (2) washers on the paper clip, and always pull the pendulum back 10.0 cm from the vertical before each timing.

5.    For each row in the table, find the average period by dividing your time for 5 swings by 5.  Enter this value under the column labeled “average period.”

 Pendulum length Time for 5 swings Average period .40 m .35 m .30 m .25 m .20 m .15 m .10 m

QUESTIONS

1.              Does the period of the simple pendulum depend on its length?  How do you know?  What can you say about this relationship?

2.              Create of graph (a sketch is okay) of length (the independent variable; on the x-axis) versus period (the dependent variable; on the y-axis).  What kind of relationship does this look like?  What kind of equation would you expect this relationship to be described by?

3.              Why did you keep two (2) washers on the paper clip?  (Similarly, why did you always pull the pendulum back a distance of 10.0 cm?)