SETTING THE PROBLEM (OSCILLATION SYNTHESIS)     

A body's movement when it is performing a simple harmonic oscillation while the basis on which it moves is also performing a simple harmonic oscillation, is called composite oscillation and its study is called oscillation synthesis.
The basis' oscillation is not neccesarily performed in the body's oscillation direction. The body's movement is generally complex. The direction, the frequency, the width and its phase depend on the relevant characteristics of the individual oscillations.      

Let us define the two oscillations:
x1(t) = A1 sin(w1 t)
x2(t) = A2 sin(w2 t + f)
where A1, A2 are the widths of the oscillations respectively, w1, w2 are the frequencies of the oscillations and f is the difference in the phase of the two oscillations.  

Note: In order to define any function or run any program or command in Mathematica, press SHIFT + ENTER or ENTER in the Num Pad.

Created by Mathematica  (November 4, 2015)