Consider the 2-DOF car suspension system model from the Modeling Mechanical
Systems notes. Define the state variables $x_1 = x$, $x_2 = \dot{x}$, $x_3 = y$, $x_4 = \dot{y}$ and convert
the two second-order ODE's, $\ddot{x} = f(x, \dot{x}, y, \dot{y}, r)$ and $\ddot{y} = f(x, \dot{x}, y, \dot{y})$, into four first-
order ODE's, $\dot{x_i} = g_i(x_1, x_2, x_3, x_4, r)$, $i = 1,2,3,4$.
Now define the following parameter values: $m_w = 20 \text{ kg}$, $m_c = 375 \text{ kg}$, $k_s =$
$130,000 \frac{N}{m}$, $k_w = 1,000,000 \frac{N}{m}$, $b = 9800 \frac{N \cdot s}{m}$, $r = 1 \text{m}$. Use the MATLAB function
ode45() to numerically solve the four first-order ODE's over the time span $[0, 1]$ s with
initial conditions $x_i(0) = 0$, $i = 1,2,3,4$. Plot the mass displacements $x_1 = x$, $x_3 = y$
over time. (Turn in both your plot and your MATLAB code.)
