Final answer:
To find the state-variable model, define the state variables as j and y, and rewrite the equation with their derivatives. The state-variable model is 2j' + j' + 12y' = Sü + 0.2u - u(t)b.
Step-by-step explanation:
A state-variable model represents a system using a set of differential equations that describe the relationships between the system's state variables and their derivatives. In this case, the system is described by the equation 2j + j + 12y = Sü + 0.2u - u(t)b. To find the state-variable model, we first need to define the state variables. Let's consider j and y as the state variables. Then, we can rewrite the equation as:
2j' + j' + 12y' = Sü + 0.2u - u(t)b
This equation, along with the definitions j' = dj/dt and y' = dy/dt, forms the state-variable model for the given system.