Draw

$($T$)$

$A^{\text{'}\text{'}}$

$$

Ask Copilot

$3$

of $6$

Question #$4(25$ points$)$: Suspension System Model

A quarter car model of a vehicle suspension is shown below. The model consists of a mass $m_1$ corresponding to a quarter of the total vehicle mass $($minus the wheels$)$ and a mass $m_2$ corresponding to a wheel. The suspension linking the vehicle body to the wheel consists of a spring of stiffness $k_1$ in parallel with a shock absorber of damping coefficient $c_1.$ Meanwhile, the wheel is modeled as having a stiffness $k_2.$ Coordinates $z_1$ and $z_2$ measure the positions of $n,$ ises $m_1$ and $m_2$ with respect to their static equilibrium positions $($i$.$e$.,$ where the springs balance the gravity forces$).$ The input to the suspension is the road surface displacement $h(t),$ which is dependent on the road profile and vehicle speed. Find the transfer function, $G(s)=\frac{Z_1(s)}{H(s)}.$