Show transcribed image text (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) = 50 sin(6) Newtons a. Solve the initial value problem. y(t) help (formulas) b. Determine the long-term behavior of the system. Is lim t)0Iit 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)