Here is the video I mentioned earlier:
The video was originally going to be 60 FPS but ended up not being so.
You can notice the stuttering at 0:29 - 0:33. This is with timestep of 60 FPS without interpolation. Notice that when the interpolation is activated, this stuttering never occurs. You can see when interpolation or extrapolation is enabled/disabled and which size timestep is currently in use by looking at the window's title bar.
You may also notice that when the timestep is at 5 FPS, using interpolation makes the movement just as smooth as with 60 FPS timestep; the only difference (in this case) is that the circle must move in larger amounts without stopping (the amount it moves without interpolation).
I'm not sure if this is the exact problem you're having but I hope it helps!
