Suppose a system of interest is given by: 5 dy(t)/dt+ y(t) – 10 u(t). With the output initially at y(0) = 0, an input of u (t) – 2t is

applied. a) After steady-state error is reached, by what duration will the output lag the input, in s? b) Suppose the output is in turn input to a different system, given by dz(t)/dt + 3 z(t) = y (t). Find the transfer function from U (s) to Z (s).dt C) Find the Laplace transform for Z (s) when u (t) = 2t.