How Do Back and Forth Movements Connect to Going Around in Oscillators?

[PremedBeauty]

In the linear oscillator the motion is "back and forth" and angular frequency suggests something "going around". Try to explain how "back and forth" is related to "going around".

This question is pertaining to the oscillator machine. It is connected with two strings, and is a cart thing with a horn on and it goes back and forth and it's suppose to represent going around. Does the back and forth relate going around in cycles?

 

[SGT]

The position at any moment is a function of the maximum amplitude and of the cosine of \omega t.
You can represent this as the projection on the x-axis of a circular movement with radius equal to the amplitude and angular frequency \omega

 

[PremedBeauty]

reply

So, how does back and forth represent going around?

 

[SGT]

Imagine an object at the edge of a spinning turntable. If you observe it from the top you will see it going around.
Now, observe it from a point of view at the plane of the turntable. You will see it going back and forth.

 

[PremedBeauty]

Hmm, I thought when it comes to oscillation "back and forth", your talking about cycles.

 

[Tomsk]

Yes, something oscillating back and forth moves in cycles. If you were to set up a spring system or pendulum that was oscillating back and forth with the same frequency as the rotating turntable, (that is it takes the same amount of time for each of them to get back to where they start) you will see them moving in unison when you look at them from the side.

 

[PremedBeauty]

Okay

Oh okay, thanks for your help you guys :):):)