If I set a particle at a known momentum and a known position, then I would expect that I know the precise position and momentum upon measurement (assuming I can measure that well). The uncertainty principle states that a known precise position means an unknown momentum. However, information cannot be created nor destroyed so somehow I am getting only 1 output from 2 inputs. This also means that this is an irreversible system. In a non-quantum example (so that I exclude the observer effect completely), I cannot know both the precise frequency and the precise time of a waveform.
If information isn't lost, could it perhaps be that I haven't given it that information in the first place, and that the information of the precise frequency and time can't exist together in the form of a wave?
Note: I am not a physics student, just a curious person. So if equations are being used, please try to explain what they represent. Thank you!