тa" + сa' + kх —DF(t), x(0) = 0, x'(0) = 0modeling the motion of a damped mass-spring system initially at rest and subjected to anapplied 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) = 80 cos(8t) Newtons.Solve the initial value problem.æ(t)help (formulas)Determine the long-term behavior of the system (steady periodic solution). Is lim x(t) = 0?If it is, enter zero. If not, enter a function that approximates x(t) for very large positive valuesof t.For very large positive values of t,æ(t) z xsp(t)help(formulas)

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modeling the motion of a damped mass-spring system initially at rest and subjected to an applied force F(t), where the unit of force is the Newton (N). Assume that m c = 8 kilograms per second, k = 80 Newtons per meter, and F(t) = 80 cos(8t) Newtons. 2 kilograms,