Question $4.$ For a system described by the transfer function

$H(s)=\frac{3s+2}{3s^2+7s+2},$

$(4$a$)$ Derive the spectrum of $H().$

$(4$b$)$ Find the system response to the input $u(t),$ where $u(t)$ is the unit step function.

$(4$c$)$ Find the system response to the sinusoidal input $cos(3t-45)u(t),$ where $u(t)$ is the unit step function.

$(4$d$)$ Find the system response to the sinusoidal input $sin(2t+60)u(t),$ where $u(t)$ is the unit step function.

$(4$e$)$ Use Matlab to plot the frequency response $H().$ Please provide your Matlab code.

$(4$f$)$ Use the Matlab function bode to produce the Bode plot of $H().$ Please provide your Matlab code.