(a) Assuming zero initial conditions, find the transfer function for a system that obeys the equation

\[\ddot{y}+4 \dot{y}+4 y=u(t) .\]

(b) From the transfer function, obtain the unit step response of the system.

(c) From the transfer function, obtain the system's impulse response.

(d) Differentiate the answer to part (a) and compare the result with the impulse response obtained in \((c)\).