So in the oscillation problems, is there difference between "mode" and "normal mode"? I know that "normal modes" are independent and orthogonal, so one doesn't affect the other. Now I am not sure when one says just "mode" is it meant on "normal mode" or is it meant on "combination of normal modes"? For example, in oscillation systems with three degrees of freedom we have three normal modes and I understand that, but when one says "mode" does he mean on one particular "normal mode" or on some combination of normal modes?

In particular, I am currently learning about the EM field in rectangular cavity and the result is that EM field inside of the cavity can have only discrete frequencies called "modes". These modes are determined by three discrete numbers due to three dimensions of the box. My teacher just says "mode" when he means on EM field (or EM standing wave) of particular frequency inside this cavity, and he says this mode (or frequency of the standing wave) is determined by three discrete numbers (one for each coordinate in 3D space). He never mentions "normal mode" so I am confused on what exactly he means by "mode".

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    $\begingroup$ I understand mode as a shorthand for normal mode. $\endgroup$ – Diracology Jul 10 '17 at 14:04
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    $\begingroup$ I can't think of a case where "mode* doesn't mean "normal mode". $\endgroup$ – DanielSank Jul 10 '17 at 15:35
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    $\begingroup$ In some cases "normal" implies a natural mode of a system (e.g., it's "normal" for a pendulum to swing). A mere "mode" may be referring to a driven oscillation that would not otherwise occur were the system not driven to produce that oscillation. However, it's generally the case that the two terms are synonymous. $\endgroup$ – honeste_vivere Jul 21 '17 at 13:23

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