The Simple Pendulum

The period of a pendulum is the time required for one oscillation (one back and forth swing). The length of a pendulum is the distance from the point of attachment to the hanging weight. The mass of a pendulum is the mass of the hanging weight. The amplitude of the pendulum is the largest angle that the pendulum cord makes with the vertical.

The pendulum is set into motion by simply releasing it from some (starting) amplitude?

What do you think?

· Will the period be different for different masses? If so, will it be less (swing faster) or greater (swing more slowly) if a heavier mass is used?

· Will the period be different for different length pendulums? Will it decrease (swing faster) or increase (swing more slowly) if a longer string is used?

· Will the period be different for different starting amplitudes?

· What factors are involved?

· How will control those factors that you are not testing?

Design experiments to test the various relationships between the period and the other properties of the pendulum. Be sure you can present verbal, numerical (tabular), and graphical representations of your findings. (HINT: If you want to determine how a property affects the period, what is the easiest way to handle the other properties?)

Available Apparatus

String, various pendulum weights (of different masses), protractor, stopwatch, meter stick, support stand for pendulum

Suggested Procedure:

Modify your experiment designs based on the available equipment.

Write a null hypothesis and your methods, then check with your instructor before beginning your experiment

Collect enough data to plot and possibly fit your data in SPSS (see pg 26 for instructions) and verbally describe the results. Describe as best you can the reasons for your results based on your understanding of the motion of bodies falling under a force due to gravity.

Follow Up Questions:

1. The period of one pendulum is 4 seconds. A second pendulum has a period of 2 seconds. Which has a longer length? Which has a larger mass? Which has a greater angle of oscillation?

2. A pendulum clock, e.g. a coo-coo clock or a grandfather clock, uses a swinging pendulum to record passing time. If a certain clock is running fast, explain how the length of the pendulum must be changed to correct this (or at least as a first attempt).

3. The frequency of a certain pendulum is 10 cycles/sec, and the frequency of another is 5 cycles/sec (the frequency equals 1/period). Which has a longer length? Which has a larger mass? Which has a greater angle of oscillation?

4. A swinging limb, e. g., an arm has a natural or unforced, relaxed, frequency of oscillation. Imagine an arm freely swinging from the shoulder. How would the period change if the arm were bent at the elbow compared to being straight?

5. A combination of many experiments and theoretical calculations have lead to the relationship: or , where T = period, L = length, and g is acceleration due to gravity. Are your results consistent with this? Fit a regression line to an (x,y) plot with and determine both the slope m and the intercept b for this line . What values of m and b would correspond to the theoretical formula? How do your values compare to these?

6. The period of a simple pendulum is 1 sec on Earth. What is its period on the moon? (Note: g_moon=1/6 g_earth)

7. When a pendulum clock that is accurate at sea level is located high in the mountains, does it gain time, lose time, or keep accurate time? Justify your answer. (HINT: Refer to your answer for #6)

8. The pendulum in a pendulum clock probably loses amplitude due to friction. Would this affect the ability of the clock to keep accurate time? Explain why or why not.

9. How does the period of a playground swing change if you stand on it rather than sit on it? Explain your answer.

You may also carry out this experiment via the web at

http://www.phy.ntnu.edu.tw/java/Pendulum/Pendulum.html