$($c$)$ The system starts at rest, $y_1^{}(0)=y_2^{}(0)=0,$ with the mass displacements at $y_1(0)=0$ and $y_2(0)=0.$ Use the MATLAB function ode $45$ to numerically solve the four $1^{st}-$order ODEs in part $($b$)$ from time $0s$ to $30s$ with parameters $m_1=1kg,m_2=1kg,k=2\frac{N}{m},b=10N*\frac{s}{m},$ and a unit step force of $F=1N($that is$,F(t)=0$ for for $t0).$ Plot $y_1(t)$ and $y_2(t)$ versus time $t$ in one figure and include a legend that identifies each plot. Label the figure axes. Hand in your code and figure with your homework.

$[$Note: You may use the code for the car suspension system model, posted on Canvas under the MATLAB Code module, as a template for your code.