Answer part $($ii$)$

$($i$)$ Fig. Q$1$ is a diagram of an accelerometer. The accelerometer mass $m$ is suspended by two springs of stiffness $k$ and two dampers with coefficient of damping $c.$ The input acceleration is $a=\frac{d^{2}x}{d{t}^2}$ as shown which results in a displacement of $y$ of the mass $m$ from its at rest position relative to the body of the accelerometer Derive the transfer function relating output displacement to input acceleration i$.$e$.,\frac{Y(s)}{A(s)}$

$(20$ marks$)$

$($ii$)$ Hence determine the natural frequency and damping ratio of the accelerometer. For an accelerometer mass of $10$ g determine the spring stiffiness $k$ that will give a natural frequency of $100$ kHz and the coefficient of damping $c$ to give a damping ratio of $0\mathrm{.}65$

$>$Answer $($ii$)$