ammar_kurd
Junior Member level 3
In the text books it's usually the angular frequency used for frequency response, can anyone tell me why? what is the advantages of using (w) instead of (f)?
Follow along with the video below to see how to install our site as a web app on your home screen.
Note: This feature may not be available in some browsers.
In the text books it's usually the angular frequency used for frequency response, can anyone tell me why? what is the advantages of using (w) instead of (f)?
Okay so frequency (f) and angular frequency (w) are two different measures of the repetation of say a sine wave, am I correct?
Hi,
W = 2 x Pi x f
The 2 x Pi come from a circle. 2 x Pi is one revolution. It is the same as 360°.
When we speak of sine full wave it is like one complete revolution.
****
Both values say different things.
Frequency is somehow an expression of time. Exactely 1/time. And the unit is 1/s.
Where w is an expression of angle/time. Unit is rad/s.
So you could also ask: why do we sometimes talk about "s" (= seconds = time) and another time we talk about "m/s" (= meter/second = speed).
But speed and time are different things, they must not be mixed.
Klaus
The equivalence is seen that a simple harmonic motion (sine or cosine wave) can be considered a the addition of two circular waves in opposite directions with same amplitude and period. In the same way, a circular motion is the sum of two simple harmonic motions in perpendicular direction (with same amplitude and frequency).
Klaus - I cannot fully agree to you.
I think, "frequency" is NOT an "expression of time". It is rather a number of occurences per time unit (frequency: periods per second) . And that is a very important difference!.
Maybe.Both are very close to each other and are parameters in the frequency domain.
This is definitely true.The invention of the angular frequency is primarily motivated by mathematical reasons (description of frequencies in the complex plane using exp(jwt).
An example that comes into my mind: 0.0000116 1/s (Hz) means once per day. So rad/s may be applied to the rotation of the earth.
But it could also mean a chicken lays an egg per day. (where i find it difficult to express this in rad/s)
I did not see that, could you give me an mathematical example ?