We are interested in examining the motion of a spring system. A mass weighing 1 kg stretches a spring 1.96 m. The mass is in a medium that exerts a viscous resistance of 4 N when the mass has a velocity of 2ms. Under the assumption; (a) Derive the system of differential equation describing the vertical motion of the mass (Use g=9.8ms). (b) Given that the initial conditions are y(0) = 2, y' (0)=-2, find the equation of motion y(t) using: (i) Laplace transform; (ii) Method in Chapter 4. (iii) Compare your answers in part (i) and (ii). What can you conclude? (c) What are the steady-state and transient terms?