= Solution
In a \b[<vibrating-sample magnetometer>], a magnetized specimen vibrates sinusoidally in a nominally uniform applied field. Its motion changes the magnetic flux through stationary pickup coils, producing an induced <voltage> by <Faraday's law of induction>. The component at the vibration frequency is proportional to the sample <magnetic moment> times vibration amplitude and frequency, for a calibrated coil geometry.
A lock-in detector referenced to the vibration extracts this small signal. Calibrate with a known moment, stabilize the vibration amplitude and sweep the applied field to measure a <magnetization> loop. Dividing moment by film volume gives $M$ in $\mathrm{A\,m^{-1}}$; the silicon substrate and holder background must be subtracted for such a thin film.<7300 Series VSM System User's Manual by Lake Shore Cryotronics>[Section 4.1: pickup signal, vibration amplitude/frequency and synchronous detection]{ref}
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