(1 point) Consider the initial value problem my′′+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), 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)=80cos(8t)
Newtons. Solve the initial value problem. y(t)= Determine the
long-term behavior of the system. Is limt→∞y(t)=0? If it is, enter
zero. If not, enter a function that approximates y(t) for...