Consider the initial value problem = my" +cy'+ky F(t), y(0) = 0, y'(0) = 0 modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force F(t), where the unit of force is the Newton (N). Assume that m = 2 kilograms, c = 8 kilograms per second, k = 80 Newtons per meter, and the applied force in Newtons is [20 F(t) = {2 if 0 t/2, if t>/2. a. Solve the initial value problem, using that the displacement y(t) and velocity y'(t) remain continuous when the applied force is discontinuous. For 0 ts/2, y(t) = Fort/2, y(t) = help (formulas) help (formulas) b. Determine the long-term behavior of the system. Is lim y(t)=0? If it is, enter zero. If not, enter a function that approximates y(t) for very large positive values of t. 817 For very large positive values of t, y(t) help (formulas)