Problems:

Suspension System Analysis Using MATLAB

For the simplified car suspension system shown in Figure $1$ where $x(t)$ is

measured with respect to the equilibrium position, use MATLAB's ode$45.$m

to plot the position of the car after the car hits a unit bump: draw the FBD$,$

derive the EOM, give your MATLAB code, and show relevant figures that

illustrate your argument for the choice of $b($e$.$g$.,$ show curves of $x(t)$ versus

$t.$ Assume that $r(t)$ is a unit step in position with $r(t)=1,r^{}(t)=0.$ Assume

that all initial conditions are zero $(x(t)=0,x^{}(t)=0),$ and that $m=350kg,k=$

$10,000\frac{N}{m}.$ Find the value of $b$ that you would prefer if you were the car

driver. Give a subjective but reasonable argument, which a $4-$year old would

Suspension System

understand, for picking one value of $b$ over another. $($Hint: try using values

of $b$ of $500N*\frac{s}{m},2000N*\frac{s}{m},5000N*\frac{s}{m}).$ This question will be used to

assess student's ability to communicate effectively with a range of audiences.