Forced Self-Sustained Oscillator

[Apteronotus]

Hi,

I'm reading about self-sustained oscillators under the influence of harmonic forcing. The topic is introduced by studying the system in a new reference frame; one which rotates in the same direction with the frequency of the of the external force.

In this new reference frame, the oscillating force is represented by a constant vector, acting at some angle. (see pg 48 http://books.google.ca/books?id=LVvUKAjXHhoC&printsec=frontcover&dq=synchronization&hl=en&ei=brLlS8bRN4GdlgfSvPztCg&sa=X&oi=book_result&ct=book-thumbnail&resnum=1&ved=0CDcQ6wEwAA#v=onepage&q=represented%20in%20the%20frame%20rotating%20with%20the%20same%20&f=false" )

At first glance, I thought the concept was trivial, but now I'm having a very hard time understanding why this would be so. Can anyone shed some light on this topic?

Thanks

ps. consider this...

--A stationary point in this reference frame is one which is oscillating in the original reference frame, with the same frequency as the force.

--The force on such a point is then said to be constant.

--However, to my understanding, the force in the original reference frame varies with time, indifferent of the objects position!

 

[Valerie Park]

The concept is that the force in the new reference frame is constant because it is "averaged" over a full cycle of the external force. In other words, if you look at the force in the new reference frame, you would be looking at the average value of the force over one cycle. This means that the force will always be the same if you look at it in the rotating reference frame. The way to think about this concept is to imagine a point on the oscillator that is rotating around in a circle along with the frequency of the external force. If you look at the force in the rotating reference frame, it will look like it is stationary and constant, even though in the original reference frame it is changing all the time.