Consider the initial value problem my" + cy' + ky = f(t), y(0) = 0, y'o) = 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 f(t) = 50 sin(6) newtons. a. solve the initial value problem. y(t) = (25/(6t)-6cos(6t))e^(2t)+sin(6t)+co s(6t))^(-2t) (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) t (formulas)