= Proof mass
A <proof mass> is an inertial element whose relative motion or required support <force> provides a measure of <acceleration>. In a spring-supported <accelerometer>, the instrument frame moves with the object being measured, while the proof mass responds through its inertia and suspension.
An ideal one-axis model is $m\ddot x+c\dot x+kx=-ma$, where $x$ is displacement relative to the frame, $m$ is the proof mass, $c$ is damping and $k$ is the <spring constant>. At frequencies well below resonance, $x\approx-ma/k$. A <capacitive accelerometer> measures this displacement electrically. The suspension determines sensitivity and bandwidth together; a more compliant spring gives greater static displacement but a lower natural frequency.<ADXL335 Data Sheet by Analog Devices>[Page10, suspended mechanical sensor and differential capacitive readout; ideal oscillator model derived here]{ref}
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