Application of an rf field at right angles to the external field results in changes that are difficult to picture clearly unless one invokes the rotating frame of reference. You need a bit of vector algebra for the explanation. We start in the laboratory frame. Picture yourself standing and watching a rotating vector:

The vector, F, rotates with angular velocity w. Our current point of view is called the laboratory frame. Obviously, w is measured relative to the laboratory frame. From the laboratory frame the motion of F is described by:

Note that I am using d/dt for the laboratory frame and ∂/∂t for the rotating frame.

If we now 'jump' on to the rotating frame and look at the vector, it will appear to be motionless:

and we can say, that from our point of view in the rotating frame:

Now, let's turn it around. Let's suppose that there is vector, G, that appears motionless in the laboratory frame:

If we view this vector from the rotating frame, which is rotating at angular frequency w, it will appear to us to be rotating with angular frequency -w:

Ok. So far so good. Now let's look at vector G from the rotating frame but this time G is moving in both the laboratory frame and the rotating frame. From our rotating frame viewpoint it will have its -w movement plus the laboratory frame movement:

or:

This is the general transformation equation from laboratory to rotating frame coordinates. Remember that d/dt refers to the laboratory frame and ∂/∂t refers to the rotating frame of coordinates.

Now, since we are interested in what is happening to the spin magnetic moment, if we put this into the equation we get:

or:

This has the same form as the expression for the laboratory frame magnetic moment:

if we replace B with the effective field, B_eff = B + w/g

We can choose any angular frequency that we like for the rotating coordinate frame but let's see what happens if we choose w to be the same as the negative of the Larmor frequency( gB):

Thus, the magnetic moment vector in the rotating frame is motionless if we choose the proper rotational frequency for the rotating frame. This turns out to be a very happy result for us.

If we are in a rotating frame which has a rotational frequency of w_R and we are viewing a vector which has rotational frequency w_F the difference in frequency is W = w_F - w_R. W is the chemical shift frequency that we are all familiar with from nmr spectroscopy.