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a) (0.5 points) When a force of 16 N is applied to a spring, the spring stretches by 4 meters. After attaching a mass of 1kg, the resulting mass-spring system is submerged in a fluid which provides a damping force equal to 4 times the instantaneous velocity. An external force f(t) = 2t is applied starting at t = 0. Briefly explain why displacement x(t) for the mass-spring system is determined by the diffeq: x" + 4x' + 4x = 2t b) (0.5 points) Suppose the mass is released at rest, 1 meter to the left of equilibrium. Write down the corresponding initial conditions for x(0) and x'(0). c) (1.5 points) Solve the IVP for the mass-spring system described in parts (a) and (b) for displacement x(t).