4. A spring-mass system with damping1 described by the equation :12\"(t) + Zy'(t) + 2y(t) = 0, is initially at rest but the mass is struck twice with a hammer: First it is struck with a unit impulse 6 at time t = at, and then it is struck with an impulse F6 at time t = T > 7r, where F 75 0. Thus, the position 22(t) of the mass obeys the symbolic IVP :1:"(t) + 23%) + 2mm = 5(t arr) + F61: - T), :c(0) = 0, az'(0) = 0. (a) (5 points) Find the position of the mass for all t 2 0. (b) (5 points) Given that T = 3a, nd the strength F such that 2:05) = 0 for all t Z T = 37r1 i.e., the second hammer strike perfectly cancels out the motion caused by the rst hammer strike