Why the frequency is so important in MEMS? c d b a Collision sensors for safety test of automobiles

Why the resonant frequency of a MEMS structure should be calculated precisely? Taking gyro as an example to describe:

Prototype sample test data Sensitivity – 39.4dB ENL: 33.6dB MEMS Microphone

Post-CMOS compatible on-chip fabrication of high-performance passives for RF SOCs Wireless Phone Inductors Capacitors Resistors Transistor Chips RF Filter (ceramic) IF Filter (SAW) RF Filter (SAW) Quartz Crystal

And how we know? Energy method for frequency

The method is quite limited!

If the force or mass is not concentrated but distributed, how can we do? df  (dx) The area Is the potential energy in the thin layer

The total mechanical energy is the sum of the potential and the kinetic ones

If the cross section is not a rectangular one, it should be a function of A(x)

Examples:

(3) With both self-weight and the end concentrated mass