(Solved): 12. The left figure below shows a MEMS accelerometer comprising one mass and two springs. The mass ...

12. The left figure below shows a MEMS accelerometer comprising one mass and two springs. The mass displacement is measured with a capacitive displacement sensor, whose output is $Vs$. This sensor can be modeled as two series capacitors as shown in the right figure. Derive from first principles (i.e from scratch) an expression for the acceleration in terms of $d,Vs$, and $Vi$.