Forced Self-Sustained Oscillator

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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" [Broken])

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!!
 
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