For the $\frac{1}{4}-$car physical

model shown:

List all physical model

simplifying assumptions.

Draw FBDs and derive the

mathematical equations of

motion for the system.

Convert the ODEs to a

transfer function

representation.

Draw a Simulink model of

the system.

Investigate the effects of

mass ratio, stiffness ratio,

and damping coefficient

ratio on vibration of $m.$

$m=500kg,m_w=50kg$

$b=3500N-\frac{s}{m},k=96k\frac{N}{m}$

$k_t=270k\frac{N}{m},b_{+}=300N-\frac{s}{m}$

$x(t)=$step$(0\mathrm{.}1m)$

$x(t)=(x_0)sin(2ft)$

$x_0=0\mathrm{.}01m,f=1Hz$