Consider the initial value problem ma" + cx' + kr = F(t), 2(0) = 0, '(0)=0 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 = 2 kilograms, e = 8 kilograms per second, k=80 Newtons per meter, and F(t) = 50e Newtons. Solve the initial value problem. z(t) = help (formulas) Determine the long-term behavior of the system (steady periodic solution). Is lim z(t) = 0? If it is, enter zero. If not, enter a function that approximates a(t) for very large positive values of t. t-00 For very large positive values of t. (t) Top(t) 0 P help (formulas)

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