A typical simple pendulum consists of a heavy pendulum bob (mass = ) suspended from a light string. It is generally assumed that the mass of the string is negligible. If the bob is pulled away from the vertical with some angle, , and released so that the pendulum swings within a vertical plane, the period of the pendulum is given as:

(1)

where is the length of the pendulum and is the acceleration due to earth's gravity. Note only the first three terms in the infinite series is given in Equation 1. The period is defined as the time required for the pendulum to complete one oscillation. That is, if the pendulum is released at some point, P, the period is defined as the time required for the pendulum to swing along its path and return to point P.

The above formula for the pendulum's period is greatly simplified if we limit the initial angle to small values. If is small, we can approximate the period of the pendulum with a first-order expression, which, in the case of our simple pendulum is given as:

(2)

Note that the period in this expression is independent of the pendulum's mass as initial angle, . It is important to understand that the above equation is valid only in the small angle approximation.

1. Determine the maximum angle for which the first-order expression (Equation 2) for the period of a simple pendulum (Equation 1) is valid. In other words, ascertain the cutoff angle for when small angle approximation fails.

2. Use a simple pendulum to determine the value of g, the acceleration due to earth's gravity.

(Figure 1.) The pendulum stand, clamp and bob. (Figure 2.) The pendulum string is secured with the pendulum clamp. Notice that it is not necessary to tie knots in the string. (Figure 3.) The pendulum bob is an aluminum rod. The bob's center of mass is marked. (Figure 4.) A protractor is used to determine the initial angle that the pendulum string makes with the vertical. (Figures 5, 6 & 7.) As the pendulum swings, a stopwatch or computer timing device is used to measure the pendulum's period. (Figures 6 & 7.) The computer timing devices shown in these figures are found on our physics lab web page (Figure 6) and also in the Lab Programs folder found on the computer desk tops of each laboratory computer (Figure 7). (Figure 8.) The meter sticks are located in the window well at the front of the classroom.

[Click on images to enlarge.] 1 2 3 4 5 6 7 8

1. Do not tie knots in the pendulum string. Instead, use the pendulum clamp to set the pendulum to the desired length.

1. Stopwatch timer
2. Clemson Physics Lab Tutorials
3. Using significant figures
4. Measurement uncertainties
5. Using Excel
6. Graphing data using Excel
7. Adding a trendline to an Excel plot
8. Fitting multiple curves (trendlines) to one data set
9. Using error bars in Excel

Each lab group should download the Lab Report Template and fill in the relevant information as you perform the experiment. Each person in the group should print-out the Questions section and answer them individually. Since each lab group will turn in an electronic copy of the lab report, be sure to rename the lab report template file. The naming convention is as follows:

For example the group at lab table #5 working on the Ideal Gas Law experiment would rename their template file as "5 Gas Law.doc".

These Nudge Questions are to be answered by your group and checked by your TA as you do the lab. They should be answered in your lab notebook.

General Nudges

1. What method did you use to determine the initial angle of the pendulum?
2. What is the uncertainty of the timing device?
3. What is the uncertainty of your measurement of the period of the pendulum?
4. What steps did you take to decrease the uncertainty in the measurement of the period?
5. What is the uncertainty in the length measurement?

1. What method will you use to determine the cut-off angle?
2. Would the length of the pendulum affect the uncertainty of the period and length measurements?

1. What parameters will you graph in order to measure g?
2. Did your best-fit line fall within the data points' error bars? Was this expected?
3. What initial angle will you use when working on the second objective?

These Questions are also found in the Lab Report Template. They must be answered by each individual of the group. This is not a team activity. Each person should attach their own copy to the lab report just prior to handing in the lab to your TA.

1. Describe how the pendulum's period is affected if the bob's mass is doubled. Halved. Assume the period is independent of .

2. Draw a free-body diagram of the pendulum at the top of this page. You may ignore friction forces. Write down the force that drives the system, that is, the force along the direction of motion.

3. A simple pendulum has a mass of 0.750kg and a length of 0.500m. What is the tension in the string when the pendulum is at an angle of 20°?

4. Show that for small angles, the driving force in Question 2 becomes . Use the fact that at small angles , and the image of the pendulum at the top of this page to help you.

5. Compare the pendulum's restoring force to the restoring force of the simple harmonic motion of an oscillating mass on a spring.

The experiment was performed and a sample write-up was "graded" by the laboratory curator. The write-up and the curator's comments are available for you to view and refer back to when you write future lab reports.

• Since the TAs were working on table #5, they saved the template as "5pendulum.doc".
• You can also view a typical page from a laboratory notebook: Word Format or PDF Format.

The data for this sample experiment is found in the sample lab report entitled "5pendulum.doc".

The questions for this sample experiment are found in the sample lab report entitled "5pendulum.doc".

As of now, there are no CUPOL experiments associated with this experiment.