Superposition of simple harmonic oscillations

[confucius]

Main Question or Discussion Point

I know how to add harmonic oscillations on the same axis but i was wondering why can i do it? If i have x1(t)=Asin(w1t +fi1) and x2(t)=Bsin(w2t +fi2), why can i say that the resultant motion is x=x1+x2. Once again im not interested in the solution because i know how to derive it but how to derive superposition of given oscillations from the fact that forces can be superposed. It is just my hunch that it has to be that. Please correct me if im wrong. Thanks for your answers and i apologise for my bad english.

 

[gsal]

I didn't think you could always do it...you can only apply superposition to linear systems.