= Solution
A carrier in a locally parabolic isotropic band obeys $m^*\dot{\mathbf v}=q\mathbf v\times\mathbf B$, so
$$
\boxed{\omega_c=\frac{|q|B}{m_c},\qquad m_c=\frac{|q|B_{\rm res}}\omega}.
$$
Illuminate a high-mobility crystal with a transverse alternating <electric field>, sweep a calibrated static <magnetic field> at known <microwave> or far-infrared <frequency>, and detect resonant absorbed <power>. Cooling lengthens the <relaxation time>; resolving the <resonance> generally needs $\omega_c\tau\gg1$. Varying field direction measures band anisotropy, while <circular polarization> distinguishes the two senses of rotation for opposite carrier charges. This is orbital motion rather than <electron> spin <resonance>.
The classic silicon/germanium measurements used single crystals near $4\ \mathrm K$, light modulation and circularly polarized <microwaves>, with directional scans to infer anisotropic carrier-energy surfaces.<Cyclotron Resonance of Electrons and Holes in Silicon and Germanium Crystals by Gene Dresselhaus and others>[Abstract: low-temperature single crystals, light modulation, circular polarization and anisotropy]{ref} Carrier generation, calibration, scattering linewidth and inhomogeneity must be separated from a genuine <mass> shift.
In a general band the cyclotron <mass> is an orbit property, $m_c=\hbar^2(\partial A_k/\partial E)/(2\pi)$ for the appropriate field-normal orbit. It need not equal every component of the band-curvature <mass> tensor. For an ellipsoidal parabolic band with field along a principal $z$ direction it is $\sqrt{m_xm_y}$. Thus a single <resonance> does not determine a whole effective-mass tensor without angular information.
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