# How to Decrease the Period of a Pendulum

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The characteristic movement of a pendulum swings an object freely back and forth, changing its direction when it reaches a maximum amplitude. The period of a pendulum is defined by the time it takes the object to travel the entire course in both directions. In order to shorten the period of a pendulum, it is helpful to first understand the mathematical equation relating the period (T) to the length (L) of the pendulum itself: T = 2 pi (L/9.8)^(1/2), where 9.8 represents the gravitational force on Earth. Alternatively, the period can also be determined as the inverse property of the frequency (f): T = 1/f.

### Things You'll Need

• Pendulum
• Tools to shorten string (may vary depending on material)

## Decrease Pendulum Length

• Look at the equation relating the period to the length of the pendulum string. Notice that these two factors are directly proportional to each other.

• Shorten the length of the string or material from which the object dangles and swings. Keep the object, pivotal point and medium the same as they were before attempting to shorten the period.

• Test the pendulum with a shortened string length. The period should be shorter than before.

## Increase the Frequency

• Recall the equation: T = 1/f. Mathematically, this proves that a higher frequency causes a shorter period.

• Push the object from its maximum amplitude with additional force in order to raise the frequency of the swinging pendulum.

• Note that accelerating the object may result in an amplitude that differs from the initial circumstance, but that amplitude has no effect on the period of a pendulum.

• Time the period to see that this method was effective, provided no factor other than the frequency was altered.

## Tips & Warnings

• Analysis of these two mathematical equations in order to identify the most important factors is important in determining the period of a pendulum.
• If you are shortening the length of a heavy or large object or pendulum, be sure to exercise caution while performing these steps.

## References

• Photo Credit Photos.com/Photos.com/Getty Images
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