Consider a mass-spring system with damping. Suppose the object has unit mass, the coefficient of friction is b = 1 and the spring constant is k = 1/2. The differential equation describing this situation is

i. Convert the 2 ^nd order DE into a first-order system in the variables y and v. plot its direction field using Bluffton and consider why solutions behave as they do in terms of the spring and damping constants.

ii. Solve the system and find the specific solution to it starting at y (0) = 1, v (0) = 2. Note y (t) is a solution to the 2 ^nd order DE.

iii. For your solution above, as t ? ? ?, what values do y (t) and v (t) approach?

dy dt + dy 1. +=y=0 dt