solve the $3$ control syseem cource question plase

Find the inverse Laplace transform of the following transfer function:

$F(s)=\frac{9}{(s-j{)}^2+81}$

seluctione

$2.f(t)=e^{-3}sin(81t)$

b$.$ None of these

c $f(t)=e^{-1t}sin(9t)$

$f(t)=e^{3t}sin(81t)$

$=f(t)=e^{3t}sin(9t)$

A syatem is described by the following differential Ecuation:

$6\frac{d^{4}y}{d{t}^4}+\frac{d^{2}y}{d{t}^2}-\frac{dy}{dt}+2y=2+\frac{du}{dt}-2\frac{d^{2}y}{d{t}^2}$

Find the transfer function of the system $Y\frac{s}{U}(s)$

Salsctone:

a None of there

b $\frac{Y(s)}{D(s)}=\frac{-2s^2+s+2}{6s^2+s^2-s-2}$

F $\frac{Y(s)}{U(s)}=\frac{-2s^2+s+2}{6s^2+s^2-s+2}$

c$.\frac{Y(s)}{V(s)}=\frac{-2s^2+s+2}{6r^3+s^2-s+2}$

a$.\frac{Y(s)}{V(s)}=\frac{-2s^2+s+2}{6s^2+s^2+s+2}$

A system is described by the following transfer function:

$F(s)=\frac{x^3+8+2}{4x^3+6x^2-3+1}$

Determine the differential aquation that governs the system.

Sekctone:

a$.4y^{}+6y^{}-y^{}+y=2u-u^{}+3u^{}$

$y+6y-y+y=2u+u^{}+3u^{}$

c$.$ None of these

$4y^{}-y^{}-6y^{}+y=2u+u^{}+3i^{}$

$=4y^{}+6y^{}-y^{}+y=2u+u^{}+3u^{}$