= Accelerometer
An <accelerometer> measures <proper acceleration>, the acceleration associated with nongravitational support and applied forces on its sensing mass. A common design suspends a <proof mass> on springs inside a housing. Housing motion displaces the mass relative to the support; a <capacitive accelerometer> reads the resulting change in <capacitance>. At frequencies well below mechanical resonance, <Hooke's law> and <Newton's second law> give displacement magnitude $|x|\simeq m|a|/k$, with <spring constant> $k$.<Low-g Accelerometers by Murata Manufacturing>[Low-g Accelerometer, spring/proof-mass structure and capacitive readout]{ref}
A simple calibration rotates a stationary sensor so one axis points up, sideways and down. Near Earth's surface, the axis reading changes approximately from $+g$ through zero to $-g$, where $g\simeq9.81\,\mathrm{m\,s^{-2}}$. A supported stationary device therefore has a nonzero reading even though its position is constant; in ideal <free fall>, the mass and housing fall together and the reading approaches zero. This experimentally separates the measured support acceleration from coordinate acceleration.<Motion sensors in the Android Developers documentation>[Use the accelerometer, stationary-table and free-fall readings]{ref}
For a horizontal ideal sensor with $m=10^{-6}\,\mathrm{kg}$ and $k=1\,\mathrm{N\,m^{-1}}$, an acceleration of $2\,\mathrm{m\,s^{-2}}$ gives a displacement magnitude of $2\,\mathrm{\mu m}$. The readout converts a tiny mechanical displacement into an electrical signal; its scale, bias and frequency response must be calibrated.
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