The state-space representation of a system is usually much easier to derive from the differential equations than Laplace transform method. Difficulties arise when the derivatives of the inputs appear in the differential equations, and this situation occurs here, which leads to a lot of algebra. At the moment we have not even determined what are good states to use. To begin, divide the first and second equations by M1 and M2 respectively.
Note appears in the equation for .
The first state will be X1 . Since the derivative of the inputs does not appear in the equation for , choose the second state to be . We then choose the third state to be the difference between X1 and X2 . After doing some algebra, we will determine what the fourth state should be. Call the integral Y2 .