Textbook Problem $5\mathrm{.}22$ but following these instructions: $($a$)$ Write the state equations $($there are two$)$

using as the states the velocity of mass $M$ and the force in spring $K_2.($b$)$ Write two output equations,

one for the position of mass $M$ and the other for the angular position of inertia wheel $J.$ Hint: Use

textbook Example $5\mathrm{.}11$ and the rotary systems lecture notes to see how to handle a rack and pinion.

$5\mathrm{.}22.$ The input to the combined translational and rotational system shown in Figure P$5\mathrm{.}22$

is the force $f_a(t)$ applied to the mass $M.$ The elements $K_1$ and $K_2$ are undeflected when

$x=0$ and $=0.$

Figure P$5\mathrm{.}22$