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# Tick Tock, Tick Tock

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Source:
Author: Janice VanCleave

Category: Physics—Mechanics—Pendulum

Project Idea by: Chris Holifield

Question: How does mass affect the period of a pendulum?

A pendulum is a device with a bob (a weight) hung from a fixed pivot (the point on which something turns) so that it swings back and forth. When a pendulum hangs so that its bob is directly below the pivot, it experiences zero net force (the sum of all forces simultaneously acting on an object) and is said to be at its resting point. When the bob is pulled to one side and released, it repeatedly swings back and forth. One back-and-forth motion is called a vibration. The pendulum's period (T) is the time required to complete one vibration. The equation for period is: period (T) = time/vibrations.

Displacement is the distance a pendulum moves to one side from its vertical position. Since the pendulum moves in an arc (a part of a circle), its displacement is an angular distance measured in degrees. The displacement angle is measured from the pendulum's vertical position. At a displacement angle of 15° or less, the periodic motion of the pendulum is the same; that is, regardless of the displacement of the pendulum, as long as it is 15° or less, the period of the pendulum will be the same.

Since weight is a measure of the gravitational pull on an object, would pendulums of different weights have different periods? As the mass of an object increases, its weight increases. A project problem might be, "How does mass affect the period of a pendulum?"

Design pendulums that are the same except for the weight of the bob. They might be washers tied to a string. You can vary the weight of the bob by using a different number of washers for each pendulum. Pull the pendulums to one side so that they all start with the same displacement. Count the oscillations in a given time period.

• Independent Variable: Weight of bobs
• Dependent Variable: Period
• Constant Variables: Length of pendulum, timing of period, displacement angle
• Control: Median-weight pendulum

### Other Questions to Explore

1. What effect does a displacement greater than 15% have on the period of a pendulum?
2. What effect does the stiffness of the bob support have on the period of a pendulum?
3. What effect does the size of the bob have on the period of a pendulum?
4. What effect does the length of a pendulum have on its period?