5. A spring is stretched 800 cm by a mass that weighs 10 N. The system is placed in a viscous medium with a damping coefficient equal to one third of the magnitude of the initial velocity. If the system is driven by an external force equal to f (t) = 3 cost N. The system is then set in motion from a point 2 m below its equilibrium position with an initial velocity of 3 m/S. Assume g = 10m/$2. a. Formulate the initial value problem. Do not solve the IVP; the solution is given below. (10 pts) b. The solution to the above IVP is: 1204 _t 1970 t 138 12 y = 533 e 2 cost + 3731 e 2 sint + 533 cost + 533 -sin t Identify the terms that represent the following (10 pts): i. The transient solution ii. The steady state solution