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

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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 Dash 1 (100.46 KiB) Viewed 66 times

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) = 30 sin(6t) Newtons. = a. Solve the initial value problem. y(t) = help (formulas) 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. t→∞ For very large positive values of t, y(t) ≈ help (formulas)