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Frequency Of Periodic Motion

Frequency of a periodic function is defined as the  number of cycles  that are completed with in a particular second. The process of repeating again and again with the equal period of distance and is known as periodic function. In this article we are going to discuss about Frequency of a periodic function. Let us consider a function with constant with constant time interval as t, then the periodic function is given by f(x+t). We know that frequency is inversely proportional to time. Let us discuss about the Frequency of a periodic function in detail with example.

   The general equation of sine wave is given by,

                                           y="sin(ax+b);


Problems for Frequency of Periodic Motion


Problem 1:

            Find the frequency of the given periodic function f(x)=0.2sin(2x+5)

Solution:

            Given periodic function f(x)=0.2sin(2x+5)

            on comparing with genera equation we get,

            Time period of the given periodic function =`(2pi)/2`

                                                                                    =`pi`

            Time period of the  periodic function =`pi`

       we know that  Frequency is  inversely proportional to time,

                        Frequency="`1/t` =`1/pi`

Problem 2:

            Find the frequency of the given periodic function f(x)=0.2sin(2`pi` x+5)

Solution:

            given periodic function f(x)=0.2sin(2`pi` x+5)

            on comparing with genera equation we get,

            time period of the given periodic function =`2*(pi)/(2pi)`

                                                                                    =1

            time period of the  periodic function =1

              we know that,Frequency is  inversely proportional to time,

                        Frequency="`1/t` =`1/1` =1

Problem 3:

Find the frequency of the given time` pi/4.`

Solution:

            Time period of the given periodic function = `pi/4`


                        Frequency is  inversely proportional to time,

                        Frequency="`1/t` =`1/(pi/4)`

                     Frequency  =`(4/pi)`


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Practice Problems


Problem 1:

            Find the frequency of the given periodic function f(x)=0.2sin(4x+5)

Answer:`2/pi`

Problem 2:

            Find the frequency of the given periodic function f(x)=0.2sin(2`pi` x+5)

Answer:1

Problem 3:

             Find the frequency of the given time `pi/2` .

Answer: `2/pi`


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