Using a single phase induction motor equivalent circuit in LTspice
I don't know the requirements for LTspice. The motor example seems reasonable, but I didn't try to check all of the details.

A slip value of 0.005 would represent a very light load. For the fan of your previous question, the slip at rated load is 0.15. You should run the simulation for various values of slip and plot the results.

Re: Added Figure 9.11

In 9.11(c), 0.5R2/(2-s) is the correct representation of the effect of the torque produced by the backward rotating field. I don't think that the initially posted equivalent circuit is wrong, but the slip terms in that figure have "f" and "b" subscripts that are not explained.

By labeling the stator components "main," figure 9.11 suggests that an auxiliary stator circuit was used for starting, but has been disconnected for the operation condition represented.