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# Periodic Motion

by Ron Kurtus (revised 29 October 2011)

Periodic motion is when the motion of an object continually repeats itself. This can be repeatedly moving back and forth or it could be moving in a circular orbit or rotation.

Since the Law of Inertia states that an object moves in a straight line unless acted upon by a force, periodic motion requires some sort of force to create this special type of motion.

Characteristics of periodic motion are the velocity of the object, the period of motion and the amplitude of the motion. Periodic motion is seen in various waveforms and is used in clocks and other devices.

Questions you may have include:

• What forces cause periodic motion?
• What are some common characteristics of this motion?
• What are periodic motion applications?

This lesson will answer those questions. Useful tool: Units Conversion

## Forces that cause periodic motion

Newton's Law of Inertia states that an object in motion will continue to move at a constant velocity in a straight line unless acted upon by an external force. There are several situations where an external force can cause an object to be in periodic motion. These include circular motion and back-and-forth motion.

### Circular or orbital motion

When you swing an object around you that is held on a rope or string, that object is in periodic motion. The force that is preventing the object from flying out in a straight line is the force you are applying on the string. Likewise, when a planet moves around the Sun, the force of gravity keeps the planet in the periodic motion around the Sun and prevents it from flying out into space.

A spinning ball is a special case, since the force is not obvious. Every atom on the ball seeks to move in a straight line, but the internal molecular forces of the ball cause them to continue to move in the periodical spinning motion.

### Back-and-forth motion

Examples of forces causing back-and-forth motion include a bouncing ball, pendulum and spring.

#### Bouncing ball

When you throw a rubber ball upward, the force of gravity pulls it back down to earth. When it hits the ground, the force of the collision changes the direction of the velocity, and the ball moves upward again, going up and down in a regular or periodic manner. A good rubber ball or a super-ball will keep bouncing for a long time. Because of internal friction and air resistance, the ball bounces less and less each time, until it finally stops. A perfect ball—without friction—would bounce forever.

#### Pendulum

If you swing a weight on a string, it will go back and forth in regular periodic motion. Once it got started, such a pendulum would move back-and-forth forever if it was not for internal friction in the string and air resistance. The force of gravity causes the pendulum bob to change directions, while the force from the string moves it in a semi-circular motion.

#### Spring

With a spring, you apply a force to compress the spring and distort the metal. The molecular forces inside the metal push in the opposite direction, causing the spring to expand. The spring then oscillates back-and-forth in a periodic motion.

A tuning fork is similar to a spring. When you strike a tuning fork, and you can see the ends vibrate back and forth. The molecular forces cause it to vibrate and the vibrations cause the air to vibrate, resulting in sound or a musical note.

## Characteristics of periodic motion

All objects that are in periodic motion have three similar characteristics: velocity, period, and amplitude.

### Velocity

They all have a velocity. You can measure the velocity of a bouncing ball, the weight on a pendulum, or such.

### Period

The period is the time the object takes to go back and forth. If you spin a weight on a string, you can measure the time it takes to go 1 revolution. Drop a ball and measure the time it takes until it bounces back up. That is its period.

Sometimes frequency is used instead of period. Frequency is the reciprocal of period. That means that frequency equals 1 divided by the time of the period or:

f = 1/t

where

• f is the frequency, measured in repetitions per second
• t is the period or time it takes for one cycle, measured in seconds

### Amplitude

The amplitude is 1/2 the distance the object goes before from one side of the period to the other. For an object in rotation, the amplitude is the radius of the circle (1/2 the diameter). The amplitude of a pendulum swing would be the distance from the bottom to the height on one side of the swing.

## Applications of periodic motion

There are many devices that use the characteristics of periodic motion. A clock is the most common device. We can also use the fact that the motion repeats itself regularly to predict what will happen, like in setting up a calendar from the Earth's periodic motion.

Another use for the knowledge of periodic motion is that it applies to the study of wave motion, including light, sound, and music.

## Summary

Periodic motion is when the motion of an object continually repeats itself, such as repeatedly moving back and forth or moving in a circular orbit. The Law of Inertia states that an object moves in a straight line unless acted upon by a force, so periodic motion requires force to create this special type of motion. Characteristics of periodic motion are the velocity, period of motion and amplitude of the motion. Periodic motion is seen in various waveforms and is used in clocks and other devices.

Many things in life swing back and forth, like a pendulum

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