Consider a system modeled by the transfer function $H(s)=\frac{1}{10s+2}$

a$)$ Calculate the response of the system to an input $u(t)=10$

b$)$ Calculate the steady$-$state response of the system to an input $u(t)=10$

c$)$ Calculate the error and the steady$-$state error of the system to an input $u(t)=10$

d$)$ Calculate the response of the system to an input $u(t)=5(t),$ where $(t)$ is the unit impulse function.

e$)$ Calculate the response of the system to an input $u(t)=10t.$

f$)$ Calculate the steady$-$state error of the system to an input $u(t)=10t.$

g$)$ Calculate the response of the system to an input $u(t)=2e^{-t}.$