The block diagram for a piezoceramic accelerometer transducer is shown

For the following values of the system parameters: $k=7\mathrm{.}74{10}^{10}\frac{N}{m},$

$WL{g}_{33}E=1\mathrm{.}16{10}^{-2}\frac{C}{m},m={10}^{-3}kg,b=0,R_c={10}^{10},C_c={10}^{3}pF,T=0\mathrm{.}5{10}^{-3}m,$

$W=12\mathrm{.}7{10}^{-3}m$ and $L=38\mathrm{.}1{10}^{-3}m,$ determine the following :

$($a$)$ The time constant of the system $=R_c{C}_c$

$($b$)$ The transfer function of the system $G(s)=\frac{v(s)}{a(s)}$