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)=40sin(6t)
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
very large positive values of t.
For very large positive values of t,
y(t)≈