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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...

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)=60cos(8t) Newtons. Solve the initial value problem. y(t)= help (formulas) 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)≈

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