(2 pts) 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) if 0<t</2, if tπ/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 tπ/2, y(t) = (1/12)(e^(-2t)) ((3*(e^(2t)))-sin(6t)-3cos(6t)) For tπ/2, y(t) = 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. For very large positive values of t, y(t) ≈ help (formulas)