What is the classical equation of motion of spinning magnetic dipole in a magnetic field? In short: what is the classical equation of motion of spinning magnetic dipole in a magnetic field?
I can't seem to find this information...
 A: In general the torque $\vec{\tau}$ of a magnetic dipole with magnetic moment $\vec{\mu}$ in a magnetic field $\vec{B}$ can be written as
$$ \vec{\tau} = \vec{\mu} \times \vec{B}$$
(see e.g. here).
The equation of motion for an angular motion is defined as
$$\vec{\tau}(t) = I \, \ddot{\theta}(t) \, \vec{e}_\perp$$
where $I$ is the moment of inertia and $\theta$ the angular displacement. Note that the direction of the torque $\vec{e}_\perp$ is perpendicular to the plain in which the movement takes place. For a general solution you have to express $\vec{\mu}$ and $\vec{B}$ in terms of $\theta$, in the following I will give you a simple example:

Image source
We assume a constant homogeneous magnetic field $\vec{B}$ in a certain direction and define $\theta(t)$ as the angle between the field $\vec{B}$ and the magnetic moment $\vec{\mu}$ (like in the graphic above). Then we simply can express the cross product as 
$$\vec{\mu} \times \vec{B} = - \mu \, B \, \sin(\theta) \, \vec{e}_\perp$$
where $\mu = |\vec{\mu}|$ and $B = |\vec{B}|$. We need the minus sign because the  torque operates in the opposite direction of the angular displacement.
Putting this together, we get the equation of motion for the angle $\theta$:
$$ I \, \ddot{\theta}(t) = - \mu \, B \, \sin(\theta(t))$$
which is similar to the equation of motion of a pendulum. For small angles you can use the approximation $\sin(\theta) \approx \theta$, which will lead to the equation of motion of a harmonic oscillator which frequency 
$$\omega_0 = \sqrt{\frac{\mu B}{I}}$$
