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# Pendulum: A Harmonic Oscillator (page 2)

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Author: Janice VanCleave

### Try New Approaches

1. How does the mass of the simple pendulum affect its period? Repeat the experiment four times, increasing the number of washers by one with each investigation. Record your results in a Pendulum: Mass vs. Period Data table like Table 11.2. Science Fair Hint: Display a photograph of the pendulum with a data table showing the average period for each mass.
2. How does the length of the pendulum affect its period? Repeat the original experiment using different lengths of string. Science Fair Hint: Display a photograph of the pendulum with a Pendulum Period vs. Length Data table.

1.
1. Gravity is the force that causes a pendulum to oscillate. As the pendulum moves down from its displaced position, it accelerates; as it rises, it decelerates. The relationship between the period and length of a pendulum and gravity is:
2. g = 4π2l/T2

where g is the acceleration of gravity, l is the length of the pendulum, and T is the period of the pendulum. Design an experiment that uses a pendulum to determine the acceleration of gravity. One way is to build a support for the pendulum that is free-standing, such as the wooden stand in Figure 11.2. The pendulum can be a string with one or more washers attached. Measure and record the length of the pendulum (which is the length from where the string is attached to the pivot to the bob's center of gravity, generally its geometric center), and use the procedure from the original experiment to determine the pendulum's period. Use the equation to calculate the acceleration of gravity. Perform the experiment five times, recording your data in a Pendulum Acceleration Data table like Table 11.3. For more information, see Karl F. Kuhn, Basic Physics: A Self Teaching Guide (New York: Wiley, 1996), pp.104-105.

3. The accepted value for the acceleration of gravity on Earth is 9.8 m/sec2. Use the average acceleration of gravity to determine the relative error in your investigation. See Appendix 2 for information on determining relative error.

### Get the Facts

1. A rigid pendulum, such as that in a clock, is called a physical pendulum. How does the period of a physical pendulum compare to that of a simple pendulum? For information, see Robert Ehrlich, Why Toast Lands Jelly-Side Down (Princeton, N.].: Princeton University Press, 1997),pp.123-124.
2. French scientist Jean Foucault (1819-1868) used a simple pendulum to demonstrate that Earth rotates on its axis. How did Foucault's pendulum prove that Earth rotates? For information, see Marc Alan Rosner, Scientific American Great Science Fair Projects (New York: Wiley, 2000), p. 115.
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