A simple accelerometer is constructed by a spring and a mass of $0\mathrm{.}1$ kg as shown in figure below. The stiffness of the

spring is $0\mathrm{.}50\frac{N}{m}m.$ Under an acceleration $a,$ the mass will displace $xmm$ from its static equilibrium position.

$($a$)$ Calculate the force $F(N)$ acting on the mass per unit acceleration in $\frac{N}{\frac{m}{s^2}}.$

$($b$)$ Calculate the displacement $x(mm)$ per unit force $F(N).$

$($c$)$ A displacement transducer is used to measure the displacement $(x)$ of the mass. It gives a voltage signal to a

galyanometer instrument having a sensitivity of $10\frac{\%}{m}V,$ the output of the galvanometer will give a deflection of $150$ to

indicate $4g$ acceleration. Draw the block diagram for the complete measurement system, and hence calculate the

sensitivity of the displacement transducer in V$/$m$.$ State all quantities, sensitivities$,$ and units on the diagram. $($Assume

there is no friction, and the gravitational acceleration $g$ is $9\mathrm{.}81\frac{m}{s^2}.)$

$(14$ marks$)$

A simple accelerometer is constructed by a spring and a mass of $0\mathrm{.}1$ kg as shown in figure below. The stiffness of the

spring is $0\mathrm{.}50\frac{N}{m}m.$ Under an acceleration $a,$ the mass will displace $xmm$ from its static equilibrium position.

$($a$)$ Calculate the force $F(N)$ acting on the mass per unit acceleration in $\frac{N}{\frac{m}{s^2}}.$

$($b$)$ Calculate the displacement $x(mm)$ per unit force $F(N).$

$($c$)$ A displacement transducer is used to measure the displacement $(x)$ of the mass. It gives a voltage signal to a

galvanometer instrument having a sensitivity of $10\frac{}{m}V,$ the output of the galvanometer will give a deflection of $150$ to

indicate $4$ g acceleration. Draw the block diagram for the complete measurement system, and hence calculate the

sensitivity of the displacement transducer in V$/$m$.$ State all quantities, sensitivities$,$ and units on the diagram. $($Assume

there is no friction, and the gravitational acceleration $g$ is $9\mathrm{.}81\frac{m}{s^2}.)$

In $3($c$)$ please show the steps on how to get the K$3=1\mathrm{.}91$v$/$m