(1 point) consider the initial value problem my′′+cy′+ky=f(t), y(0)=0, y′(0)=0 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)f(t), where the unit of force is the newton (n). assume that m=2m=2 kilograms, c=8c=8 kilograms per second, k=80k=80 newtons per meter, and the applied force in newtons is f(t)={300if 0≤t≤π/2,if t> π/2. f(t)={30if 0≤t≤π/2,0if t> π/2. solve the initial value problem, using that the displacement y(t)y(t) and velocity y′(t)y′(t) remain continuous when the applied force is discontinuous. for 0≤t≤π/20≤t≤π/2, y(t)=y(t)= (formulas) for t> π/2t> π/2, y(t)=y(t)= (formulas) determine the long-term behavior of the system. is limt→[infinity]y(t)=0limt→[infinity ]y(t)=0? if it is, enter zero. if not, enter a function that approximates y(t)y(t) for very large positive values of tt. for very large positive values of tt, y(t)≈y(t)≈ (formulas)