Consider the initial value problem

my+cy+ky=F(t),y(0)=0,y(0)=0my+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)F(t), where the unit of force is the Newton (N). Assume that m=2m=2 kilograms, c=8c=8 kilograms per second, k=80k=80 Newtons per meter, and F(t)=40cos(8t)F(t)=40cos(8t) Newtons.

1. Solve the initial value problem.
2. Determine the long-term behavior of the system. Is limty(t)=0limty(t)=0? If it is, enter zero. If not, enter a function that approximates y(t)y(t) for very large positive values of tt. For very large positive values of t, y(t)