4. Consider a mass spring system with m = k = 1 and 2(0) = 2'0) = 0. At each of the instants t=0,1,2,3,..., ,.., the mass is struck a hammer blow with a unit impulse. Thus the position function of the mass satisfies the IVP z" +1 = 8(t-na), 7(0) = x'(0) = 0. Applying the Laplace Transform we obtain X6w) = so that the solution is r(t) = u(t - nn) sin( t n ). Because sin( t n ) = (-1)" sint and ut - 1) = 0 for t