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Main » Kinematics & Dynamics » Understanding Motion » Periodic Motion

### Understanding Motion - Periodic Motion

 Key Terms: Vibration | Period (T) | Frequency (f) | Dot Interval |

 Periodic Motion is motion that repeats itself at regular intervals of time. The pendulum in a grandfather clock and a weight on a string spinning around in circles exhibit periodic motion. The Earth rotates around the Sun in a periodic circular motion.Example: Solar System motion  Example: Balls Colliding If you drop a ball, it will start to bounce in a regular fashion. 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. This is also an example of periodic motion. Click and drag the ball and release the ball at a certain height in the flash example. Example: Ball and Gravity

Brainstorm with a classmate and find 5 more objects that display periodic motion.

We now must become familiar with some basic terminology, which is used to describe this type of motion.

 Vibration (N) - One complete to and fro motion. Period (T) - The length of time required for one vibration. It is expressed in seconds. Frequency (f) - The numbe of vibrations per unit time. One vibration per second is one hertz (Hz).

Note:

For a recording timer a record of periodic motion occurs when the striker hits the recording tape at regular intervals. The space between the dots on a recording tape is called one dot interval. One vibration is represented by one dot interval.

Sample Problem 1

What is the Period of a pendulum in a grandfather clock if it takes 17s to make 11 vibrations?

Sample Problem 2

If it takes 13s to make 72 vibrations of the striker, what is the frequency of the timer?

When you look at the equations for the period and the frequency of the timer you will notice that these quantities have an inverse relationship which can be stated mathematically as:

Sample Problem 3

A recording timer was used to make a permanent record of motion on a recording tape. Christopher counted 267 dot intervals between the starting line and the finish line on the tape. It took 3.6 s for the tape to pass beneath the striker from start to finish.

Calculate the:
 frequency of the timer. period of the timer. change in time between the third and sixth dot (see Image A). number of dot intervals for a change in time of 1.2 s. number of dots for a change in time of 1.2 s. Image A: