Limit the framerate to a high but stable amount. The game config has a custom option for how high you want the framerate to go. Try setting it to 600fps or 480fps, a multiple of your monitor's refresh rate to make sure it's smooth (I assume you're using 60hz). It is recommended to just run it at unlimited. If you're fluctuating around 1000-1200 fps that doesn't matter, it's too insignificant to matter. If you're fluctuating around 1000fps to 200fps that is where you're going to have problems. That you can remedy by trying to see if your pc has power saving options set up and disable them. If after all that and you're still getting unstable framerates then It may be something with your gpu cooling not working properly and trying to throttle itself to not burn up.
human responsive is around 250 - 300ms, so a little ms don't really effect you, it's about stable. You force the fps to 1k+, but it's stable or not ? FPS jumping around 1200 -> 1000 is not stable.What the hell are you saying? Ignore this guy he doesn't know what he's talking about. Human "responsive", or response time I'm guessing is what you're trying to say, has nothing to do with how osu! plays as you're not reacting. Everything that has higher latency will add up and make it feel like you're moving around while drunk. Monitor response time is NOT AT ALL tied to display latency. What the game runs at and the monitor displays at are two separate things that add up as I said.
Second is your monitor, is your monitor can support 1ms responsive or not ? If you monitor just support up to 4 or 5 ms, force your machine to 1k fps simply not worth it.