Caution: you cannot trust OpAmps at high frequencies. They cannot control their Vout, and you'll get surprised.
An Impulse is a useful input signal, because active LowPassFilters will let some of that Impulse appear on OpAmp's output. WaltJung warned of this. We honor WaltJung in the canned-example tool called Signal Wave Explorer; simply click the topleft "examples" button, select "Beware the Active Filter", then drop to bottomleft and click "Run". You'll learn that enabling/disabling C1 is the key to successful "filtering" of an impulse.
Where
Where do impulses occur? Consider an LCD display, where 10 nanosecond RowDrivers couple into the magnetic loops of a touch-screen pen tracker.
Installing C1 was the key to success for that project.
You can download Signal Wave Explorer, for free, from robustcircuitdesign.com