Consider the initial value problem
mx??+cx?+kx=F(t), x(0)=0, x?(0)=0
modeling the motion of a spring-mass-dashpot system initially atrest and subjected to an applied force F(t), where the unit offorce is the Newton (N). Assume that m=2 kilograms, c=8 kilogramsper second, k=80 Newtons per meter, and F(t)=80cos(8t)Newtons.
Solve the initial value problem.
x(t)=
Determine the long-term behavior of the system. Is limt??x(t)=0? Ifit is, enter zero. If not, enter a function that approximates x(t)for very large positive values of t.
For very large positive values of t, x(t)?
