1 X(s) P(s) s+4s+k impulsive input p(t) = 8 (t) is applied. Assuming the initial conditions are 0. A dynamic system has a transfer function as G(s) = At t=0, an xcitation. (a) If k = 13, find the output x(t) as a function of time t. (b) If k = 13, what is the damping condition of this system (over, under, or critically)? (c) Set the value of k to make the system critically damped.