Q1: Consider the mass-spring oscillator without friction: y" + y = 0. Suppose we add a force which corresponds to push (to the left) of the mass as it oscillates. We suppose that push is described by f(t) = -h(t 2n) + u(t (2n + a)) For some a > 2n which are allowed to vary. Solve the problem by Laplace: y" +y = f(t),y(0) = 1, y'(0) = 0.