4. A springmass system with damping, described by the equation :1:"(t) + 2y'(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 5 at time t = it, and then it is struck with an impulse F5 at time t = T > gr, where F 35 0. Thus, the position $(t) of the mass obeys the symbolic NP 0. 1:\"(t) + 213%) + 2:1:(t) = 6(t rr) + F66 T), 53(0) = 0, 3:10) (a) (5 points) Find the position of the mass for all t 2 0. (b) (5 points) Given that T = 3%, nd the strength F such that t) 2 {l for all t 2 T 2 3w, i.e., the second hammer strike perfectly cancels out the motion caused by the rst hammer strike