PHYS 1111L - Introductory Physics Laboratory I

Laboratory Advanced Sheet
Pendulum Laboratory

1. Objective. The objective of this laboratory is to experimentally determine the relationships between the mass and length of a simple pendulum, and its period.

2. Theory.

a. A simple pendulum consists of a mass connected to a pivot by a string. If the pendulum is placed in motion by pulling the mass to the side and releasing it, the pendulum will oscillate back and forth. The period of the pendulum is the amount of time required for the pendulum to complete a full oscillation; that is, the time to return to its release point. For reasons that will become apparent in future physics courses, the angle of release for the pendulum should not exceed 15 degrees from the vertical.

b. By measuring the period of the simple pendulum as a function of mass and distance from pivot to center of mass of the mass, the dependence of the period on these two variables will be experimentally determined. The dependence will be reported using the following equation:

T = c m^a L^b

where

T is the period of the pendulum,
m is the mass of the pendulum,
L is the length of pendulum,
a and b are exponents that are constants and that are unitless, and
c is a constant of proportionality.

c. Relying upon our knowledge of the simplicity of functional relationships in simple physical systems, the possible values of the constants, a and b, are expected to be:

a = ± n/2

where n = 0, 1, 2, 3, ...

b = ± m/2

where m = 0, 1, 2, 3, ...

d. Two experiments will be performed. In the first, the length of the pendulum will be held constant while the mass of the pendulum is varied and the period measured; in the second, the mass of the pendulum will be held constant while the length of the pendulum is varied and the period measured. Thus, in the first experiment,

T = c₁ m^a

and in the second,

T = c₂ L^b

where c₁ and c₂ are constants.

If graphs of T versus m and T versus L are constructed, the values of a and b can be determined by performing power law fits to the data sets. Once the values of a and b are determined the constant, c, can be calculated.

3. Apparatus and experimental procedures.

a. Equipment.

1) Stop watch.

2) Meter stick.

3) String.

4) Rods and clamps.

5) Mass set.

6) Mass balance.

7) Protractor.

b. Experimental setup. The experimental setup is shown in Figure 1 (provided by the student).

c. Capabilities. To be provided by the student.

4. Requirements.

a. In the laboratory.

1) Devise an experiment to examine the effect of mass on the period of a simple pendulum. Discuss your proposed experiment with your instructor before taking measurements. Record data and present your results graphically (a graph of period versus mass with a power law fit).

2) Devise an experiment to examine the effect of the length of the pendulum (pivot to center of mass distance) on the period of a simple pendulum. Discuss your proposed experiment with your instructor before taking measurements. Record data and present results graphically (a graph of period versus length with a power law fit).

b. After the laboratory. Complete the following portions of the laboratory report.

Para. 3. Apparatus and experimental procedures.

1) Provide a figure showing the experimental setup.

2) Provide a description of the capabilities of the equipment used in the experiment.

Para. 4. Data.

1) Provide a copy of your data for the mass dependence experiment.

2) Provide a copy of your data for the length dependence experiment.

3) Provide a graph of period versus mass with power law fit.

4) Provide a graph of period versus length with power law fit.

5) Provide calculations showing the determination of the value of the constant, c, in the following equation:

T = c m^a L^b

Para. 5. Results and Conclusions.

1) Provide a statement of the dependence of the period of a simple pendulum on the mass of the pendulum.

2) Provide a statement of the dependence of the period of a simple pendulum on the length of the pendulum.

3) Provide a statement of the value of the constant of proportionality, c, in the relationship for the dependence of the period of a simple pendulum on its mass and length (do not forget the units of c).

4) Describe sources of random error in the experiment.

5) Describe sources of systematic error in the experiment.

Last update: October 28, 1998