A 4 ft a spring measures 8ft long after an 8 lb weight is attached to it. The medium through which the weight moves offers a resistance numerically equal to sqrt(2) times the instantaneous velocity.

(a) Find the equation of motion if the weight is released from the equilibrium position with a down-wards velocity of 5ft / s_{1} [15 marks]

(b) Find the time for which the weight attains its extreme displacement from the equilibrium position. 15 marks]

(c) What is the position of the weight at this instant?

(5 marks]