The camera in your cell phone must focus within t = 0.25 of being "aimed", and the lens must remain static (within 0.005mm of final position). Suppose the movement of the mechanism is a damped spring-mass system satisfying the equation (time (t) in seconds, and displacement (y) in mm).

y\"+sy'+13y = o {a} If for a particular situation yl) = .1,y'{il) = D, and the in-focus location is y = , compute the exact solution for y\"). {13) Does this meet the requirement above? If not, which coefcient in the equation would need to be changed and how? (c) For comparison, write this linear DE as two first-order DES. A time step of t = {105 is sufficiently small, and compute out to t m 2. {cl} Use an Euler scheme to solve this equation with the same initial conditions. {e} Compare and comment {show the two plots on the same axes with time out to t = 3)