14. (a) A spring with a mass of 2 kg has natural length 0.5 m. A force of 25.6 N is required to maintain it stretched to a length of 0.7 m. If the spring is stretched to a length of 0.7 m and then released with initial velocity of zero, find the position of the mass at any time t. (b) Suppose that the spring is then immersed in a fluid with damping constant c = 40. Find the position of the mass at any time t if it starts from the equilibrium position and is given a push to start it with an initial velocity of 0.6 m/s. (c) Suppose an external force F(t) = 2 cos 3t is then applied to mass. Find the position of the mass at t= if it is stretched to a length of 1 m and then released with an initial velocity of 1 m/s.