# Difficulty - Signals and Systems

## Main Question or Discussion Point

Hi
In my notes I came across the following sentences:-
Any signal consisting of the system's characteristic mode is sustained by the system on its own. The system offers no obstacle to this signal.
Not getting what it means. Please, a little help needed. :-)

Thanks
salil

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A characteristic mode is simply a natural oscillation pattern the system possesses. If you add energy to a system which is NOT in one of the system's natural oscillation patterns, then that energy will not be continually absorbed over time. For example, if you are pushing someone on a swing and the frequency you are pushing does not match the natural frequency of the swing, then you won't make any notable progress getting the swing going. But if you add energy at the 'characteristic mode' of the swing (the right spectrum of frequencies), then it will be continually absorbed causing the swing amplitude to increase. If there is an energy waster (like an electrical resistor, brake, wind resistance, etc.) in the system then I'm not sure I'd use the word "sustained" as they do in the statement, but I think the general point is that that energy will be absorbed by the system.

AlephZero