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)=30sin(6t) newtons.1. solve the initial value problem. y(t)=? 2. determine the long term behavior of the system.