Question 10 (7 marks) An object of mass 1kg is attached to a spring hanging vertically from a fixed support. The spring has spring constant / = 50 N m-. In equilibrium, the spring is stretched a distance s m. Assume that the gravitational constant is g = 10 m s-2. The system is subject to a damping force with damping constant 3 = 10 N s m . In addition, a constant downward external force of f = 100 N is exerted on the object. Let y(t) be the displacement in metres of the object below the system's equilibrium position at time & seconds. At { = 0 the object is released from rest, 0.2m below its equilibrium position. (a) Use Newton's 2nd law to show that the equation of motion for the system is y" + 10y' + 50y = 100. Include a diagram of the system at a time when the object is below its equilibrium position and moving up, with all forces shown and labelled.(b) State the initial conditions, in terms of y and y'. (c) Let v(t) = y'(t) be the velocity of the object. Differentiate the equation of motion to obtain a second-order ODE for v(t). (d) Show that v'(0) = 90