(1 point) Consider the initial value problem my" + cy' + ky = F(t), y(0) = 0, y'(0) = 0 modeling the motion of a spring-

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1 Point Consider The Initial Value Problem My Cy Ky F T Y 0 0 Y 0 0 Modeling The Motion Of A Spring 1 (247.61 KiB) Viewed 70 times

(1 point) 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) = 40et Newtons. = a. Solve the initial value problem. y(t) = help (formulas) t→∞ b. Determine the long-term behavior of the system. Is lim 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) ≈ help (formulas)