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)=100cos(8t) Newtons. Solve the initial value problem. y(t)= help (formulas) Determine the long-term behavior of the system. Is limt→[infinity]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)

You have two photos of a person walking. one shows the person at the corner of third and main streets, the other shows the person at the corner of tenth and main streets. there are lampposts at every corner in this town, and the first picture shows it to be 10: 32: 00 exactly. the second picture shows it to be 10: 49: 30. you know three facts: (1) all of the clocks are synchronized; (2) there are exactly 12 equal-sized blocks per kilometer in this town; and (3) the streets that cross main in this area are numbered consecutively, with no interruptions. what is the person’s average speed in kilometers per hour?