Question: Consider the initial value problem ++=(),(0)=0,(0)=0 modelling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force (), where the

Consider the initial value problem

++=(),(0)=0,(0)=0

modelling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force (), where the unit of force is the Newton (N). Assume that =2 kilograms, =8 kilograms per second, =80 Newtons per meter, and ()=40cos(8) Newtons.

a)Solve the initial value problem.

y(t) = ?

b) Determine the long-term behavior of the system. Is lim()=0? If it is, enter zero. If not, enter a function that approximates () for very large positive values of .

For very large positive values of , () ?

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