A spring-mass system with damping, described by the equation x" + 2x' + 2x = 0, is initially at rest but the mass is struck twice with a hammer: First it is struck with a unit impulse d at time t = , and then it is struck with an impulse Fd at time t =T > a, where F +0. Thus, the position x(t) of the mass obeys the symbolic IVP X" + 2x' + 2x = (t 7) + F(t T), x(0) = 0, x'(0) = 0. (a) (8 points) Find the position x(t) of the mass for all t > 0. (b) (8 points) Given that T = 37, find the strength F such that x(t) = 0 for all t > T = 377, i.e., the second hammer strike perfectly cancels out the motion caused by the first hammer strike