2.6.1 Capacitor microphone Capacitor microphone is an electromechanical system with two degrees of freedom: . qi=g; the electrical charge is the generalized coordinate for the electrical tank (LC series), and q2=x; the displacement from equilibrium point xo is the generalized coordinate for the mechanical tank (M, K: moving plate-spring) Fig. 2.18 capacitor microphone system A Xo-X Fixel Plate Moving Plate S(0) B The capacitor C' is given by C = where & is the dielectric constant of the air (F/m); A is the area of the plate, xo is the separation between the armatures when the microphone is not receiving any human voice; and x - x is the plate separation after a displacement x. Find the dynamic equation of the system by using: 1- Newton's and Kirchhoff 's Laws 2- Lagrange's Laws 3- Deduce the state equation of the system Indication: mx+ Bx + Kx- 92 = f 2 & A 1 La + Rq+(x - x)q=v & A