Pulsed NMR change in magnetisation vector
In the nmr experiment the sample is placed into an intense but static magnetic field. By the (nuclear) Zeeman effect the spin energy levels that are degenerate in the absence of a magnetic field become split in energy and thus more spins reside in the lower energy levels that in higher one. The number of any level is given by the Boltzmann distribution at the prevailing temperature. The total spin angular momentum of the sample is called the magnetization. To make a measurement a magnetic field from a radio frequency source is applied at right angles to the large, static field. This tips the magnetization into the x-y plane making measurements possible. I try to explain how and what happens below.

The spins have a magnetic moment $\bar m$, which is a vector quantity meaning it has direction and magnitude, and as a result the static field causes magnetic induction $\bar B$ in the sample. This is also a vector. The magnetic induction (confusingly but commonly also called the magnetic field) is induced in the sample by the the large static magnetic field often labelled $H$. 

If all the individual spin moments are added up these form the magnetization $ \bar M$. This is a magnetic field and is also a vector and so has both magnitude and direction.    All nuclear spin magnetic moments experiences a torque ( a rotational motion generating angular momentum ) in a magnetic field and is given by classical electromagnetism as $\bar m \times \bar B$ where $\times $ means this is a vector cross product; $\bar M \times \bar B=|M\|B|\sin(\theta)$ where $\theta$ is the angle between the vectors.  The change in angular momentum produced is given by $\displaystyle \frac{d\bar L}{dt}=\bar m\times B$. As the angular momentum is given by $\bar m=\gamma \bar L $,   where $\gamma$ is the magnetogyric ratio (these are known and for H is $27.75\cdot 10^{7}$ rad/T/s), then 

$$ \frac{d\bar M}{dt}=\gamma \bar M\times B \tag{1}$$

This equation can be broken down into components in x, y and z directions. The z direction is conventionally taken as the direction along which $\bar B$ lies, and this has no x or y components. The three equations produced are 

$$\frac{d M_x}{dt}=\gamma m_xB;\quad \frac{d M_y}{dt}=-\gamma m_yB; \quad \frac{d M_z}{dt}=0  \tag{2}$$

If there is no external perturbation then these equations show that the magnetization remains along the z axis and as we place the detector along the x or y axis then no signal can be observed. This is  because the magnetic field of the magnetization has to 'cut the coils' of the detector as so induce a signal that can be measured. It clearly cannot do this if it has magnitude only along the z axis.

The equations (2) can be solved if some initial conditions at time zero are chosen and physically important solutions are found only when the x and y components are not initially zero. In that case the solutions show that then magnetization in x and and y are proportional to $\sin(\omega_0t)$ and $\cos(\omega_0t)$ respectively where $\omega_0= \gamma B_0$ where $B_0$ is the z component of $\bar B$. The Larmor frequency is $\nu_0=\omega_0/(2\pi)$ and is the frequency measured in an nmr experiment. 

As these solutions require that the magnetization has to be in the x-y plane this  condition has to be satisfied and is done so by exciting the sample with rf radiation directed along the x (or y) axis. This radiation has a magnetic  field that is weak compared to $\bar B$ and of magnitude $B_1$; its frequency we will call $\omega_r$. Classically the magnetic field applies a torque to the magnetization and rotates it away from the z axis.  In a molecular (quantum) explanation, if the rf energy is resonant with the energy gap, formed by the large static field $B$, then spins are excited from the lower to upper level and this changes both the size and direction of the magnetization $\bar M$. 

In a classical  explanation the  polarised rf field $B_1$ is considered to be composed to two oppositely rotating fields. One moves in the same sense as the magnetization precesses, and so interacts with it, the other moves in the opposite sense and has little interaction and can be ignored. The experiment is now such that the spins experience both a static magnetic field $\bar B \equiv B_0$ in the z direction and a rotating field $B_1$ in the x-y plane. Clearly this is now a very complex problem but can be simplified if one assumes that the axes x and y rotate about z at the frequency of the $B_1$ magnetic field. This is called the 'rotating frame'. The result is that the equations similar to (1) are produced but with $B_{x,y,z} $ replaced by $B_{eff(x,y,z)}$ where $\displaystyle B_{eff}^2=(B_0-\frac{\omega_r}{\gamma})^2+B_1^2$.