1. (a) (5 points) Use the Laplace transform method to solve the IVP y" + 3y' + 2 =128(t -2), y(0) = 2, y' (0) = -2. (b) (5 points) Solve the same initial value problem except this time replace the right-hand side of the differential equation by g(t) = tuz(t). That is, solve y" (t) + 3y' (t) + 2y(t) = tuz(t), y(0) = 2, y'(0) = -2. 2. A spring-mass system with damping, described by the equation a" + 2x' + 2x = 0, is initially at rest but the mass is struck twice with a hammer: First it is struck with a unit impulse o at time t = 7, and then it is struck with an impulse Fo at time t = T >