(1 point) Consider the initial value problem = my" cyky 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 the applied force in Newtons is 40 if 0 ≤t ≤ π/2, F(t) = 0 ift > /2. a. Solve the initial value problem, using that the displacement y(t) and velocity '(t) remain continuous when the applied force is discontinuous. For 0 ≤1/2, y(t) = e^(-2t)(-1/2 cos(6t)-1/6sin(6t))+1/2 help (formulas) Fort/2, y(t) = 0 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. For very large positive values of t, y(t) 0 1-00 help (formulas)