Consider the initial value problem my" + cy' + kyF(t), (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, e-8 kilograms per second, k=80 Newtons per meter, and F(t) = 60 cos(8t) Newtons a. Solve the initial value problem. y(t) = 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 1x0 values of t For very large positive values of t. (f) help (formulas)