Consider the attached loudspeaker system. Let the input be the voltage $u(t)=v_a(t),$ the output be the speed of the cone $y(t)=\frac{dx}{dt}=px(t)=x^{},$ and let the state variables be

$w_1=x(t),$ cone position;

$w_2=\frac{dx}{dt},$ cone speed;

$w_3=i(t),$ current through the inductor.

a$.$ Write the corresponding state and output equations: $w^{}=Aw+bu$;$,y=c^{T}w+du$

b$.$ Draw the simulation diagram corresponding to $($a$)$