Entered Answer Preview Result [(3*[4*sin(8*t)-3*cos(8*1)]*[e (2*t)]-13*sin(6*t)+9*cos(6*t))*[e^(-2*t)]]/15 (3(4 sin(8t) - 3 cos(8t)) e2t - 13 sin(6t) + 9 cos(6t)) e-2t correct 15 incorrect At least one of the answers above is NOT correct. 1 of the questions remains unanswered. (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 F(t) = 80 cos(8t) Newtons a. Solve the initial value problem. y(t) = (3(4sin(8t)-3cos(8t))e^(2t)-13sin(6t)+9cos(6t))e^(-2t)/15 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. 1-+ 0o For very large positive values of t, y(t) ~ help (formulas)