Question $1(15$ points$)$: The dynamics of a process are described by the ODE:

$5\frac{d^{2}y(t)}{d{t}^2}+2\frac{dy(t)}{dt}+y(t)=3u(t)$

a$)$ Determine the transfer function, $G_p(s)$ :

b$)$ Find the characteristic equation:

c$)$ Apply the Rooth criteria to determine system stability and explain your conclusion.

d$)$ Plot the poles of the characteristic equation on the s$-$domain to show stability.