Hello again,
Here are a couple of root locus plots for your original circuit. The first plot shows a more continuous graph but it's harder to pick out the right value of K where the plot crosses the imaginary axis, so the second plot was done with K stepping by 5k for each dot, starting at 10k. The values labeled on the plot are in k ohms.
Looking at the second plot which also has values of K labeled, we can see that the locus crosses the imaginary axis near the point where K is approximately equal to 26.5k. We can then read off the jw frequency from the imaginary axis, divide by 2*pi, and get the frequency, which comes out in the neighborhood of 1000Hz. Higher resolution would get us closer to the exact value, but this plot was done assuming a perfect op amp anyway so the real life value of K required for oscillation would be a bit higher. Still, it's interesting to look at the plot and see what information we can get from it.