Consider the initial value problem my" + cy' + ky=F(t), y(0) 0, '(0) 0 modelling 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, e = 8 kilograms per second, k=80 Newtons per meter, and the applied force in Newtons is F(t)=(50 to fost≤ x/2, ift > */2. a. Solve the initial value problem, using that the displacement y(t) and velocity y' (t) remain continuous when the applied force is discontinuous. For 0 st≤ x/2, y(t) help (formulas) Fort > m/2, 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. For very large positive values of t. y(t) help (formulas)