1. The problem statement, all variables and given/known data Solve the DE for y(t) with the IC's y(0)=20.8m/s and y'(0)=0 if the input is a step function scaled by the desired velocity Vo. vd(t)=Vou(t). Assume the desired velocity Vo=27.8m/s 2. Relevant equations y''(t) + (D/M)y'(t) + (K/M)y(t) = (K/M)vd(t) M = 1,000kg D = 100kg/s K = controller gain y(t) = output velocity vd is the input function 3. The attempt at a solution So I'm Laplace transforming the whole 2nd order equation and I end up with a mess. The next problem is to find the optimal controller gain K for a desired response. My Laplace transform of the 2nd order equation is: Y(s) = [ KVo + Ms2y(0) + Dsy(0) ] / [ s2 + (D/M)s + (K/M) ] if in fact i'm doing it correctly, here is where i am stuck.