What Are the Equations of Motion for the Print Head Control System?

[eh87]

Homework Statement
Please refer to the image attached for problem statement and diagram.

There's an inductor somewhere, but I have no idea where and I don't know how to accommodate for it. I can also see that there's another energy storage device, the spring on the right.

I have no idea where to start with the equations of motion, but I know how to put them in SS form. If someone would help me with the equations (i.e. point me in the right direction to get me started), that would be great!

 

[kataya]

There's an inductor somewhere, but I have no idea where and I don't know how to accommodate for it

What?

This is purely mechanical. You want to find x(t), the time history of the block (print head). The best way to do this is to write it as a differential equation and solve that. So..

$$Mx'' = \Sigma(forces) = -bx' - kx + \frac{\tau(t)}{r}$$

You can then put this in state space (just define the state variables).

 

[eh87]

Hey thanks for your help.

The second part of the problem asks for a transfer function of X(s)/V(s) and he said in class that there's an inductor somewhere with inductance L and resistance R, so I know for sure there's an electrical part to it somewhere.