Consider the following values for the circuit components: $R=8,L=2H,C=\frac{1}{6}F.$ Using MATLAB find and plot the Zero$-$Input Response, Zero$-$State Response, Impulse Response, and Total Response assuming $v_0(t)=2,v_0(t)=0$ and the input voltage $v_i(t)=u(t).$ Present MATLAB code and the plots. Explain the obtained graphs.

Find the system transfer function $H(s).$ Present the hand calculations below.

Consider the following values for the circuit components: $R=8,L=2H,C=\frac{1}{6}F.$ Using the MATLAB Control System Toolbox and the Linear System Analyzer Applications, plot the system Step Response and the Impulse Response. Present MATLAB code and the related plots. Plot the step responses in part $3.$ and part $5.$ in the same plot and do the same for the impulse responses. Do the step responses in $3.$ and $5.$ match? Do the impulse responses in $3.$ and $5.$ match? Is that what you expect? Answer $3,4$ and $5$