The following schematic depicts a common motion control syst

The following schematic depicts a common motion control system such as a gantry crane moving a shipping container horizontally. Here driving force F is the input and the displacement x_2 is the output. (A) Derive the equations of motion. (B) Express these equations in state space form. (C) Generate a single differential equation to give the input output representation for this system.

Solution

Answer is C.

Because for motion of the X2 is denpend on the displacment of X1

The velocity is directly proportional to acceleration so the we have to take derivative of velocity i.e.X1 and we get the X2 value.

From given data we can findout the X1 as mention above point