# Period And Frequency In Physics

## Explanation of the period and frequency. Sample questions related to period and frequency, and solutions of these questions. Finding the period of objects that making circular motion.

**What Is Periodic Motion**

Motion of an object that does same motion perpetual is called periodic motion.

Periodic motion is repeat perpetual in a fixed interval time. It is is called period of the motion to this fixed interval time.

Period is an interval time. its unit is seconds. The period is represented by T.

Example, The motion of a constantly moving object at a fixed speed on circular path is a periodic motion. If we mark a point on the circular path,each passage of the object will be is after a period of time.

Motion of the generator and dynamo are periodic motion.

Motion of the pendulum is a periodic motion.

The motion of the minute-hand and hour-hand of an o'clock is a periodic motion.

**Example:**

The green colored object seen in the figure is turning at a fixed speed on a circular path.

The motion of this object is periodic motion. If it is 5 seconds the time elapsed until the object reached K point again after the object pass on the point K, the period of the object is 5 seconds.

**Example:**

In the figure, a simple pendulum is seen. If the pendulum doing motion its in between A and B point and completes its all motion at the same time intervals, the motion of the pendulum is a periodic motion.

Suppose that the pendulum in the figure doing periodic motion. if the pendulum comes to the point "B" from the point "A" at t time, it goes the point "A" from the point "B" at t time.

The period of this pendulum is 2t. For t = 5 second, the period is 10 second.

The time elapsed for the pendulum to go from point "A" to point "B" and from point "B" to point "A" is 1 period.

**Example:**

Rotation of the earth around its own axis is a periodic motion. The earth completes its one full rotation around its own axis at 24 hours.

Rotation of the earth around the sun axis is a periodic motion. The earth completes its one full rotation around the sun axis at 365 days 6 hours.

**Concept of Frequency**

Number of motions per 1 second of an object that does periodic motion is called the frequency.

The frequency is inverse of the period. It is represented by f.

f = | 1 | |

T |

T = | 1 | |

f |

If an object completes its one full motion at 3 seconds, its period is 3 second. This object does 1/3 of its full motion at 1 second.

The period of the object is

T = 3 s

Frequency of the object is

f = | 1 | |

T |

f = | 1 | |

3 |

**Calculations of The Period and Frequency**

**Example:**

The object "K" seen in the figure is starting to its movement on its circular path. The object "K" is moving for 1 hours and stops.

The object is doing 18000 rounds throughout its motion. Find the period and frequency of this object.

**Solution:**

The object has made 18000 rounds during 1 hours. We will find number of rounds that it done at 1 second.

1 h = 60 min = 3600 sec

One hour is 3600 seconds. To find number of rounds that it done, we are divide the 18000 into 3600. The value we will find is the frequency of the object.

f = | 18000 | |

3600 |

f = 5 Hz

The object has done 5 rounds in 1 second. Now, let we find period of the object.

T = | 1 | |

f |

T = | 1 | |

5 |

T = 0.2 s

Period of the object is 0.2 seconds.

**Example:**

Period of an object which does circular motion at a constant speed is 0.04 s.

How many rounds does this object during 1 minutes.

**Solution:**

The object is completes its one full rotation at 0.04 seconds. To find number of rounds that the object does at 1 minutes, we must find the number of rounds that the object does at 1 second.

The number of rounds at 1 second is frequency of the object.

f = | 1 | |

T |

f = | 1 | |

0.04 |

f = | 100 | |

4 |

f = 25 Hz

The object does 25 rounds at 1 seconds.

1 minutes is 60 seconds.

R = 25*60

R = 1500 rounds.

The object does 1500 rounds at 1 minutes.

**Example:**

A generator rotates at a fixed speed. The generator shaft completes its own one full rotate at 0.0167 seconds.

Find the period and frequency of this generator.

**Solution:**

If the generator shaft completing its one full rotate at 0.0167 seconds, period of this generator is 0.0167 seconds.

The frequency is inverse of the period.

f = | 1 | |

0.0167 |

f = 59.8 Hz.

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November 15 2018

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