(1 point) Consider the initial value problem my " +cy' t 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 F(t) = if 0 /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 T/2, y(t) = (-e"(-21))(1+e"(pi))(1/4cos(6t)+1/4sin(6t)) 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)