Im new to state space and need to know why in the attached jpeg is

x1(dot) = x2

x2(dot) = -k/mx1 - b/mx2 + 1/mu

 

What is it you don't understand exactly? The author had already specified the system dynamics equations and he let
\(x_1=y
x_2=\dot{y}\)

After that it's just substitutions.