Students turning in this lab for a grade need not to rewrite the questions. Include the work from calculation, data tables, and answers to questions in the order given. It is sometimes simpler to print this lab first and complete it by hand than return the computer and send it as an Email.

 

The Simple Pendulum

INTRODUCTION

In the “Measurement Lab”, the simple pendulum was used to make measurements of length and time to acquire knowledge about the concepts of percent error and percent difference. This experiment, a continuation of the “Measurement Lab”, will be concerned with how the period of a simple pendulum varies with the length of the pendulum, the mass of the bob, and the magnitude of the bob’s displacement from the equilibrium position.

Pendulums are classified as compound or simple. The compound pendulum is one in which the mass of the pendulum is distributed throughout its length. Examples are the pendulum in a grandfather clock and a meter stick held at one end and allowed to swing back and forth. A simple pendulum is one in which the mass of the pendulum is concentrated at a point. It is obvious that the mass of a simple pendulum cannot be located at a point, since a point is defined as position without dimensions. However, the length of the string or wire supporting the mass (called the bob) can be large in comparison with the diameter of the bob. Figure 3.1 illustrates the parameters of a simple pendulum.

The equation showing the relationship between the parameters of a simple pendulum is

where T the period

L = the length

g = the acceleration due to gravity = 9.8 m/s2 = 980 cm/s2 = 32 ft/s2 When both sides of the equation are squared, we obtain

 

 Note: Mass does not appear in this equation.

 LEARNING OBJECTIVES

After completing this experiment, you should be able to do the following:

1.      State the difference between a simple and a compound pendulum.

2.      Name the parameters that determine the period of a simple pendulum.

3.      Determine experimentally the parameter values for a simple pendulum.

4.      State how the period of a simple pendulum varies with the (a) length of the pendulum, (b) mass of the bob, and (c) magnitude of the displacement.

5.      Calculate the length or period for a simple pendulum when one or the other is given.

 

APPARATUS

Two different masses for pendulum bobs (hook weights, rings, rocks, etc can be used if regular bobs are not available), string, a 2-m stick (a 1-m stick  or tape measure may be used here ), stopwatch or electric timer, balance, and support holder.

 

PROCEDURE 1

This procedure is for determining the period of a simple pendulum for various lengths.

Step 1a. Construct a simple pendulum by attaching the bob to length of string. Use either given mass (call this mass number one) and make the length of the pendulum for this first step fairly large (160 cm) or whatever is reasonably possible with the means of support you have for the pendulum. The length is the distance from the point of support to the center of the bob.

Stetp 1b. Displace the pendulum bob approximately 16 cm from its equilibrium position (center position). If you use a length other than 160 cm, use a length-of-arc-to-pendulum-length ratio of 1:10. That is, displace the pendulum bob one-tenth the value of the pendulum length. Determine the time it takes for the pendulum to swing through 10 complete cycles. Before you start your timer) allow the bob to swing through a few cycles. Caution: Do not count the first cycle until one cycle has been completed. When the timer is turned on, say “start”; then when the bob comes back to this same position) say “one.” The best place to start is at one of the end points of the swing where the bob is stopped momentarily. Make three trials and record the data in Data Table 3.1. From the data calculate the period of the pendulum and record its value in the data table.

Step 1c. Adjust the length of the pendulum to 80 cm or one-half the length used in Step 1. Complete three trials for the time of 10 cycles, and record the data in Data Table 3.1. From the data calculate the period of the pendulum and record this in the data table. Remember the length of arc is to be approximately one-tenth the length of the pendulum.

Description of first mass ________________________________________

Data Table (for Procedure 1)

Time in Seconds for 10* _______Cycles 

Length of
Pendulum
(cm) 

Trial 1

Trial 2

Trial 3

Average
for Three
Trials

Time of
One Cycle Period (s) 

Period2
(s)2 

160* or

_______

 

 

 

 

 

 

80* or

_______

 

 

 

 

 

 

40* or

_______

 

 

 

 

 

 

20* or

______

 

 

 

 

 

 

*Cross out this value and insert correct value, if different.

 

Step 1d. Adjust the length of the pendulum to 40 cm or one-fourth the length used in Step 1. Displace the pendulum bob 4 cm or one-tenth the value of the pendulum length you used. Complete three trials for the time of 10 cycles and record the data in Data Table 3.1. Caution: Allow the pendulum to swing through enough cycles so that a minimum of l0s are required. If the time for 10 complete cycles is less than 10 s, then allow the pendulum to swing through 20 complete cycles for the time measurement.

 

Step 1e. Construct a graph with the period of the pendulum in seconds (y axis) versus the length of the pendulum in centimeters (x axis). A good graphing program that is not to hard to use is Microsoft graph located in Microsoft Word. In Word click on insert than object, than Microsoft Graph. From here you put data in the table, you need to remove the sample data. As you place the data in the table the graph is constructed at the same time for viewing. Once finished you can change the style of the graph by clicking on chart type at the top. Be aware if you click outside the graph or table you go back to document mode and do not have the option of changing data. To correct this just double click on the graph and you are placed back in graph mode.

 

Step 1f. Square all calculated periods and record them in Data Table 3.1. Construct a graph with the

period squared (seconds)2 on the y axis and the length (centimeters) of the pendulum on the x axis.

Determine the slope of the curve. Show your work plus the numerical value with units on the graph.

 

PROCEDURE 2

This procedure is for determining the period of a simple pendulum for a different mass. Repeat Procedure 1 using a heavier wieght. Make sure the length of the pendulum is measured from the point of support to the center of the bob. Record the data in Data Table, and compare the periods with those in Data Table 3.1.

Data Table 3.2 (for Procedure 2)

Description of second mass _________________________________________

 Data table for procedure 2.

Time in Seconds for 10* __________Cycles

 

 Length of
Pendulum
(cm)

Trial 1

Trial 2

Trial 3__—

Average
for Three
Trials

 Time of
One Cycle Period (S) 

Period2
(s)2 

160* or

______

 

 

 

 

 

 

80* or

______

 

 

 

 

 

 

40* or

______

 

 

 

 

 

 

20* or

_______

 

 

 

 

 

 

*Cross out this value and insert correct value, if different.

 

PROCEDURE 3

This procedure is for determining the period of a simple pendulum for various displacements of the pendulum bob.

Step 3a. Construct a simple pendulum as shown in Fig. 3.1. Use mass number two and make the length of the pendulum 160 cm or the same length you used in Procedure 1, Step 1. Displace the pendulum bob 16 cm or one-tenth the pendulum length you used. Make three trials and record the data in Data Table 3.3. From the data calculate the period of the pendulum and record in the data table. Note: For this length of pendulum, the period should be the same as you recorded in Data Tables 3.1 and 3.2.

Step 3b Using the same length and mass as in Step 1, displace the pendulum bob 32 cm from its equilibrium position or one-fifth the pendulum length you used. Make three trials and record the data in Data Table 3.3. From the data calculate the period of the pendulum and record in the data table.

Step 3c. epeat Step 2 displacing the pendulum bob 48 cm from its equilibrium position or three-tenths the pendulum length you used. Record all data in Data Table 3.3.

Step 3d. Repeat Step 2 displacing the pendulum bob 64 cm or four-tenths the pendulum length you used. Record all data in Data Table 3.3.

 

Length of pendulum _________ cm;

Time in Seconds for 10* __________ Cycles

Data Table (for Procedure 3)

Initial Displaced Length of Arc (cm)

Trial 1

Trial 2

Trial 3

Average for Three Trials

Period (Time of One Cycle) in s

16* or

______

______

 

 

 

 

 

32* or

______

______

 

 

 

 

 

48* or

______

______

 

 

 

 

 

64 or

______

______

 

 

 

 

 

*Cross out this value and insert correct value, if different.

 

QUESTIONS

1.    Why do you think you were asked to complete more cycles in Procedure 1, Step 3, if the total time was less than 10 s for 10 cycles?

 

 

2.    What type of graph (straight line, parabola, hyperbola) was obtained in Procedure 1, Step 5?

 

 

3. Which variable (period or length) does the graph show to be increasing the fastest? (Note: If they were increasing at the same rate, the graph would be a straight line.

 

 

4. What type of graph was obtained in Procedure 1, Step 6?

 

 

5. State how the period of the simple pendulum v aried experimentally with the (a) length of the pendulum, (b) length of arc (displacement of the bob), and (c) mass of the bob.

 

 

6. A simple pendulum has a length L and a period T. If the length is increased to 4L, What will be the new period? Refer to data tables for the answer.